Krsna divided Himself into "two" just so He could experience loving intimate association and exchanges with a women. That Women is Srimati Radharani.

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī". (Srimad Bhagavatam Canto 3 Chapter 31 text 38, Purport)

Love can only exist when "two" are involved in loving reciprocations and exchanges. 

Srila Prabhupada - ''We have got the propensity to love. Love means somebody else. Love cannot be "one" or love cannot be executed by only one, there must be another one. I love somebody; somebody loves me, there must be lover, there must be beloved, and the transaction, then love''. (Lecture on Srimad Bhagavatam Canto 1 Chapter 2 text 6, Delhi, November 12, 1973)

Srila Prabhupāda – ''Love means a relationship between two persons, then there is exchange, then there is love. I must deal with you open-hearted, you must deal with me open-hearted, then there is love. So if you want to love Kṛṣṇa, God, then these things must be there". (August 9, 1976, Tehran)

Srila Prabhupada - ''Love means you take and you give also. Suppose if you love somebody and you simply take from him, but you don't give. Oh, do you think it is very good? No. It is not good. That is NOT love. That is exploitation. If I go on simply taking from you, and if I don't offer you anything, that is simply exploitation. (Lecture on BG Chapter 9 text 2-5, New York, Nov 23, 1966)

Krsna is ALWAYS complete in Himself and is NEVER alone because within Krsna is EVERYTHING, and therefore can become two personalities or more anytime He likes.

For example, Krsna is always enjoying in Vrindavana with His consort Srimati Radharani, who Krsna created by dividing Himself into two, just so He could experience loving exchanges with a women.

In this way Krsna is "FULLY COMPLETE" as Himself due to enjoying unlimited pastimes with-

1 - With His internal energy headed by Srimati Radharani. (Sakti-Visnu-tattva) 

2 - His Visnu-tattva expansions (unlimited Visnu/Narayana expansions each with different names) 

Both Sakti-Visnu-tattvas and Visnu-tattvas have 93.75% of Krsna's qualities which is 60 of Krsna's 64 attributes.

The above two categories ARE direct expansions of Krsna where He is playing a different role in His own pastimes.

3 - His Siva-tattva expansions (many personalities who are expansions of Siva) who has 84.375% of Krsna's qualities has 55 of Krsna's 64 attributes.

4 - His jiva-tattva expansions (marginal living entities or jiva-souls) who have 78.125% of Krsna's qualities which is having 50 of Krsna's 64 attributes.

These two (Siva-tattva and the jiva-tattva souls) can NEVER be God (Visnu-tattva) meaning they are NOT Sakti-Visnu-tattva (internal potency lead by Srimati Radharani) or Visnu-tattva (Visnu/Narayana expansions of Krsna)

As said above, Siva has 84.375% of Krsns's qualities which is 55 of Krsna's 64 attributes.

The jiva-souls have 78.125% of Krsna's qualities which is 50 of Krsna's 64 attributes.

Both Siva and the jiva-souls have their own unique independent personalities separate from Krsna's Personality.

So they can NEVER be God like Krsna and His Visnu/Narayana expansions. 

The living entities manifest in different categories as Krsna's energies and can NEVER be separated from Krsna. 

This is because they are eternally linked together just like the Sun-disc and the Sun-rays exist together and can NEVER be separated from each other with the Sun-disc being the source of the Sun-rays (sunshine).

Krsna's greatest pleasure comes from Srimati Radharani His eternal consort.

Krsna is NEVER alone due to EVERYTHING being completely situated within Him making Krsna the Supreme Personality of Godhead and cause of ALL causes.

Krsna is "simultaneously one and different" from His energies, as an independent individual Person, and as His different expansions also. 

Krsna is EVERYTHING and EVERYTHING is part and parcel of Him.

This is Krsna's full potential as the Supreme controller, who is always fully satisfied within Himself, as everything is His part and parcels, making Krsna fully satisfied and complete as Himself and NEVER alone.

Krsna IS the Supreme Lord AS His own individual bodily (vigraha) Form, yet simultaneously is the source of ALL other living entities, just like the Sun-disc is the source of the Sun-rays that radiate from the Sun-disc.

And as said above, Krsna's most intimate expansion is Srimati Radharani.

Srila Prabhupada - "Rādhā and Kṛṣṇa are "one and the same", but They have assumed two bodies. Thus They enjoy each other, tasting the mellows of love. 

The two transcendentalists Rādhā and Kṛṣṇa are a puzzle to materialists. 

The description of Rādhā and Kṛṣṇa from the diary of Śrīla Svarūpa Dāmodara Gosvāmī is a condensed explanation, but one needs great spiritual insight to understand the mystery of these two personalities.

One is enjoying in two.

Śrī Kṛṣṇa is the potent factor, and Śrīmatī Rādhārāṇī is the internal potency. According to Vedānta philosophy, there is no difference between the potent and the potency; they are identical. 

We cannot differentiate between one and the other, any more than we can separate fire from heat.

Everything in the Absolute is inconceivable in relative existence. Therefore in relative cognizance it is very difficult to assimilate this truth of the oneness between the potent and the potency.

The philosophy of inconceivable oneness and difference propounded by Lord Caitanya is the only source of understanding for such intricacies of transcendence. 

In fact, Rādhārāṇī is the internal potency of Śrī Kṛṣṇa, and She eternally intensifies the pleasure of Śrī Kṛṣṇa.

Impersonalists cannot understand this without the help of a mahā-bhāgavata devotee. 

The very name “Rādhā” suggests that Śrīmatī Rādhārāṇī is eternally the topmost mistress of the comforts of Śrī Kṛṣṇa. 

As such, She is the medium transmitting the living entities’ service to Śrī Kṛṣṇa. 

Devotees in Vṛndāvana therefore seek the mercy of Śrīmatī Rādhārāṇī in order to be recognized as loving servitors of Śrī Kṛṣṇa". (Caitanya Caritamrita Adi 4.56, Translation and Purport)

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī". (Srimad Bhagavatam Canto 3 Chapter 31 text 38 Purport)

Krsna divided Himself into "two" just so He could experience loving exchanges with a women. 

Obviously loving exchanges can only exist when there are two or more involved in loving reciprocation, therefore Krsna has unlimited expansions to experience these loving relationships with.

As explained above, every living entity is part and parcel of Krsna and He accompanies every living in the material worlds as Paramatma, therefore Krsna or the living entities are NEVER alone.

This is the reality of Krsna (God) consciousness.  

For even Krsna, understanding love with can never be understood by Krsna alone, there MUST be "two", the loved and the beloved. And that exchange of loving intimacy and emotions is with Srimati Radharani. 

Therefore when Krsna wanted to experience loving emotions and affection with a women, He divided Himself into "two", just so He could experience those loving exchanges and feelings.

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī. 

It is explained by the Gosvāmīs that Rādhārāṇī is the manifestation of the pleasure potency of the Supreme Personality of Godhead. 

When the Supreme Lord wants to derive transcendental pleasure, He has to create a woman from His internal potency and that women is Srimati Radharani" (Srimad Bhagavatam Canto 3 Chapter 31 text 38, Purport)

Śrī Kṛṣṇa - “All the inhabitants of Vṛndāvana-dhāma—My mother, father, cowherd boyfriends and everything else—are like My life and soul. And among all the inhabitants of Vṛndāvana, the gopīs are My very life and soul. 

And among the gopīs, You, Śrīmatī Rādhārāṇī, are the chief. Therefore You are the very life of My life. 

Śrīmatī Rādhārāṇī is the center of all Vṛndāvana’s activities. In Vṛndāvana, Kṛṣṇa is the instrument of Śrīmatī Rādhārāṇī; therefore all the inhabitants of Vṛndāvana still chant “Jaya Rādhe!” (Caitanya Caritamrta Madhya 13.150, Translation)

Srila Prabhupada - "From Kṛṣṇa’s own statement given above, it appears that Rādhārāṇī is the Queen of Vṛndāvana and that Kṛṣṇa is simply Her decoration. 

Kṛṣṇa is known as Madana-mohana, the enchanter of Cupid, but Śrīmatī Rādhārāṇī is the enchanter of Kṛṣṇa. 

Consequently Śrīmatī Rādhārāṇī is called Madana-mohana-mohinī, the enchanter of the enchanter of Cupid". (Caitanya Caritamrta Madhya 13.150, Translation and Purport)

"Of all the gopīs, Śrīmatī Rādhārāṇī is the chief. She is a jewel mine of ecstatic love and the source of all purified ptranscendental conjugal mellows". (Caitanya Caritamrta Madhya 14.160, Translation)

Of all the gopīs, Rādhārāṇī is the dearmost. Similarly, the lake known as Rādhā-kuṇḍa is very dear to the Lord because it is very dear to Śrīmatī Rādhārāṇī". (Caitanya Caritamrta Madhya 18.7, Translation)

"Lord Kṛṣṇa, the Supreme Personality of Godhead, who appeared as the son of Nanda Mahārāja, is the supreme hero in all dealings. Similarly, Śrīmatī Rādhārāṇī is the topmost heroine in all dealings". (Caitanya Caritamrta Madhya 23.66, Translation)

"The transcendental goddess Śrīmatī Rādhārāṇī is the direct counterpart of Lord Śrī Kṛṣṇa. She is the central figure for all the goddesses of fortune. 

She possesses all the attraction to attract the all-attractive Personality of Godhead. She is the primeval internal potency of the Lord". (Caitanya Caritamrta Madhya 23.68, Translation)

"Śrīmatī Rādhārāṇī is the Ganges in which the elephant of My mind enjoys pastimes. She is the shining of the full autumn moon for the cakora birds of My eyes. 

She is the dazzling ornament, the bright and beautiful arrangement of stars, on the border of the sky of My chest. 

Now today I have gained Śrīmatī Rādhārāṇī because of the highly elevated state of My mind". (Caitanya Caritamrita Antya 1.191, Translation)

Srila Prabhupada - "Kṛṣṇa and Rādhārāṇī are both transcendentally qualified, and both of Them attract one another. 

Yet in that transcendental attraction, Rādhārāṇī is GREATER than Kṛṣṇa, for the attractiveness of Rādhārāṇī is the transcendental taste in conjugal love. 

Similarly, there are transcendental tastes in servitude, friendship and other relationships with Kṛṣṇa. 

Rādhārāṇī is the only gopī who is dearer to Kṛṣṇa than all the other gopīs". (Teachings of Lord Caitanya, Chapter 14, Purport)

Srila Prabhupada - "Lord Caitanya exhibited the mode of Śrīmatī Rādhārāṇī when She was contacted from Dvārakā by Śrī Kṛṣṇa. 

Such transcendental love is not possible for any common man; therefore one should not imitate the highest perfectional stage exhibited by Caitanya Mahāprabhu. 

If, however, one desires to be in that association, he may follow in the footsteps of the gopīs. In the Padma Purāṇa it is stated that just as Rādhārāṇī is dear to Kṛṣṇa, similarly the kuṇḍa known as Rādhākuṇḍa is also very dear to Him. 

Rādhārāṇī is the only gopī who is dearer to Kṛṣṇa than all the other gopīs. 

In Śrīmad-Bhāgavatam (10.30.28) it is also stated that Rādhārāṇī and the gopīs render the highest perfectional loving service to the Lord and that the Lord is so pleased with them that He does not wish to leave the company of Śrīmatī Rādhārāṇī". (Teachings of Lord Caitanya, Chapter 30)

Srila Prabhupada - "As Kṛṣṇa is the highest emblem of spiritual perfection, so Rādhārāṇī is the highest emblem of that spiritual pleasure potency by which Kṛṣṇa is satisfied. 

Since Kṛṣṇa is unlimited, in order to satisfy Him Rādhārāṇī is also unlimited. 

Kṛṣṇa is satisfied just by seeing Rādhārāṇī, but Rādhārāṇī expands Herself in such a way that Kṛṣṇa desires to enjoy Her more. 

Because Kṛṣṇa was unable to estimate the pleasure potency of Rādhārāṇī, He decided to accept the role of Rādhārāṇī, and that combination is Śrī Caitanya Mahāprabhu". (Teachings of Lord Caitanya, Chapter 31)

Srila Prabhupada - "When Kṛṣṇa left Vṛndāvana for Mathurā, the gopīs became most dejected and spent the rest of their lives simply crying in separation from Kṛṣṇa. 

This means that in one sense they were never actually separated from Kṛṣṇa. There is no difference between thinking of Kṛṣṇa and associating with Him. 

Rather, vipralambha-sevā, thinking of Kṛṣṇa in separation, as Śrī Caitanya Mahāprabhu did, is far better than serving Kṛṣṇa directly. 

Thus of all the devotees who have developed unalloyed devotional love for Kṛṣṇa, the gopīs are most exalted, and out of all these exalted gopīs, Śrīmatī Rādhārāṇī is the highest. 

No one can excel the devotional service of Śrīmatī Rādhārāṇī. 

Indeed, even Kṛṣṇa cannot understand the attitude of Śrīmatī Rādhārāṇī; therefore He took Her position and appeared as Śrī Caitanya Mahāprabhu, just to understand Her transcendental feelings. 

In this way Śrīla Rūpa Gosvāmī gradually concludes that Śrīmatī Rādhārāṇī is the most exalted devotee of Kṛṣṇa and that Her kuṇḍa (lake), Śrī Rādhā-kuṇḍa, is the most exalted place". (Nectar of Instruction 10, Purport)

Srila Prabhupada - "So our business is that we have to take shelter. Instead of taking shelter of the external energy... That is also Kṛṣṇa. 

There is no doubt. Kṛṣṇa, Kṛṣṇa's energy: nondifferent. But that is not very beneficial to us, we have to take shelter of the internal energy. Mahātmānas tu māṁ pārtha daivīṁ prakṛtim āśritāḥ [Bg. 9.13]. 

Daivīṁ prakṛtim means internal energy. And Śrīmatī Rādhārāṇī is the symbol of internal energy. 

Therefore we take shelter of Śrīmatī Rādhārāṇī in Vṛndāvana, and that is our perfection of life. 

Then it will be easier to associate with Kṛṣṇa very easily. That should be our motto". (Lecture on BG 4.11 -- Vrndavana, August 3, 1974)

Srila Prabhupada - "We are Kṛṣṇa’s parts and parcels and have been created to give pleasure to Kṛṣṇa. The chief pleasure potency is Rādhārāṇī, and so Rādhā-Kṛṣṇa are always together. 

Whereas the material energy is conducted by the external potency, Māyā, the spiritual world is conducted by the internal potency, Rādhārāṇī. 

We often pray to Rādhārāṇī because She is the pleasure potency of Kṛṣṇa. The very word “Kṛṣṇa” means all-attractive, but Rādhārāṇī is so great that She attracts Kṛṣṇa. 

If Kṛṣṇa is always attractive to everyone, and Rādhārāṇī is attractive to Kṛṣṇa, how can we imagine the position of Śrīmatī Rādhārāṇī? 

We should try humbly to understand and offer Her our obeisances, saying, 

“Rādhārāṇī, You are so dear to Kṛṣṇa. You are the daughter of King Vṛṣabhānu, and You are Kṛṣṇa’s beloved. We offer our respectful obeisances unto You."

Rādhārāṇī is very dear to Kṛṣṇa, and if we approach Kṛṣṇa through the mercy of Rādhārāṇī, we can easily attain Him. 

If Rādhārāṇī recommends a devotee, Kṛṣṇa immediately accepts him, however foolish he may be. 

Consequently in Vṛndāvana we find that devotees chant Rādhārāṇī’s name more often than Kṛṣṇa’s. Wherever we go in India we will find devotees calling, “Jaya Rādhe.” 

We should be more interested in worshiping Rādhārāṇī, for however fallen we may be, if somehow or other we can please Her, we can very easily understand Kṛṣṇa. 

If we try to understand Kṛṣṇa by the speculative process, we will have to spend many lifetimes of speculation; but if we take to devotional service and just try to please Rādhārāṇī, then Kṛṣṇa can be very easily realized.

Rādhārāṇī is such a great devotee that She can deliver Kṛṣṇa." (From Elevation to Krsna Consciousness, chapter 5 Knowing Krsna's Energies) .*^