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At that time there were 6 major schools of Vedic philosophy all arguing and contending with each other and with the Chārvāka - materialists, and others that have disappeared from the pages of history. The most organised religion of the time and the major contender with Brahmanism was Jainism. So the aspirant Gautama entered into a playing field with many other contenders.
They are lived together, discussed together argued (as Indians do) supported the Vedas, refuted the Vedas - rejected the Vedas and so on. Since they all lived in the same cultural milieu they all shared some common philosophical ideas and concepts of:
Dharma which was the main point of common reference. There was a prolific cross-pollination of ideas.
So from this common fecund intellectual pool comprised of Brahmanism and its competitors and antagonists three streams arose in order of their consolidation (1) Jainism (2) Buddhism and (3) what was later come to be known as Hinduism which unlike the previous two never developed a formal organizational structure.
Interestingly enough all three religions referred to themselves as Sanātana Dharma or severally as Jina-dharma, Buddha-dharma, and Vaidika-dharma — “Buddhism” and “Hinduism” were appellations given by Western scholars.