The tree's leaves are the prime factors of the number at the top. Based on the distinct multiplicities of different prime factors, it is possible to work out which colors correspond to which primes, given that each circle should correspond to a two digit number, as suggested.
This produced red = 2, orange = 3, yellow = 5, green = 11, blue = 13, indigo = 41, and violet = 67. (The colors are also sorted in ROYGBIV order from smallest to largest primes.)
The circled nodes are the products of the primes beneath them, cluing 6 2-digit numbers: 66, 82, 65, 76, 67, 72 Each number is an ASCII code for an upper-case letter of the answer: BRANCH.