jajñe suyaśasaḥ sutān
dattaṁ durvāsasaṁ somam
Anasūyā, the wife of Atri Muni, gave birth to three very famous sons — Soma, Dattātreya and Durvāsā — who were partial representations of Lord Viṣṇu, Lord Śiva and Lord Brahmā. Soma was a partial representation of Lord Brahmā, Dattātreya was a partial representation of Lord Viṣṇu, and Durvāsā was a partial representation of Lord Śiva.
In this verse we find the words ātma-īśa-brahma-sambhavān. Ātma means the Supersoul, or Viṣṇu, īśa means Lord Śiva, and brahma means the four-headed Lord Brahmā. The three sons born of Anasūyā — Dattātreya, Durvāsā and Soma — were born as partial representations of these three demigods. Ātma is not in the category of the demigods or living entities because He is Viṣṇu; therefore He is described as vibhinnāṁśa-bhūtānām. The Supersoul, Viṣṇu, is the seed-giving father of all living entities, including Brahmā and Lord Śiva. Another meaning of the word ātma may be accepted in this way: the principle who is the Supersoul in every ātmā — or, one may say, the soul of everyone — became manifested as Dattātreya, because the word aṁśa, “part and parcel,” is used here.
In Bhagavad-gītā the individual souls are also described as parts of the Supreme Personality of Godhead, or Supersoul, so why not accept that Dattātreya was one of those parts? Lord Śiva and Lord Brahmā are also described here as parts, so why not accept all of them as ordinary individual souls? The answer is that the manifestations of Viṣṇu and those of the ordinary living entities are certainly all parts and parcels of the Supreme Lord, and no one is equal to Him, but among the parts and parcels there are different categories. In the Varāha Purāṇa it is nicely explained that some of the parts are svāṁśa and some are vibhinnāṁśa. Vibhinnāṁśa parts are called jīvas, and svāṁśa parts are in the Viṣṇu category. In the jīva category, the vibhinnāṁśa parts and parcels, there are also gradations. That is explained in the Viṣṇu Purāṇa, where it is clearly stated that the individual parts and parcels of the Supreme Lord are subject to being covered by the external energy, called illusion, or māyā. Such individual parts and parcels, who can travel to any part of the Lord’s creation, are called sarva-gata and are suffering the pangs of material existence. They are proportionately freed from the coverings of ignorance under material existence according to different levels of work and under different influences of the modes of material nature. For example, the sufferings of jīvas situated in the mode of goodness are less than those of jīvas situated in the mode of ignorance. Pure Kṛṣṇa consciousness, however, is the birthright of all living entities because every living entity is part and parcel of the Supreme Lord. The consciousness of the Lord is also in the part and parcel, and according to the proportion to which that consciousness is cleared of material dirt, the living entities are differently situated. In the Vedānta-sūtra, the living entities of different gradations are compared to candles or lamps with different candlepower. For example, some electric bulbs have the power of one thousand candles, some have the power of five hundred candles, some the power of one hundred candles, some fifty candles, etc., but all electric bulbs have light. Light is present in every bulb, but the gradations of light are different. Similarly, there are gradations of Brahman. The Viṣṇu svāṁśa expansions of the Supreme Lord in different Viṣṇu forms are like lamps, Lord Śiva is also like a lamp, and the supreme candlepower, or the one-hundred-percent light, is Kṛṣṇa. The viṣṇu-tattva has ninety-four percent, the śiva-tattva has eighty-four percent, Lord Brahmā has seventy-eight percent, and the living entities are also like Brahmā, but in the conditioned state their power is still more dim. There are gradations of Brahman, and no one can deny this fact. Therefore the words ātmeśa-brahma-sambhavān indicate that Dattātreya was directly part and parcel of Viṣṇu, whereas Durvāsā and Soma were parts and parcels of Lord Śiva and Lord Brahmā.