13 is already prime. It doesn't need a rainbow.
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13 is not a factor of 126.
Yes, 13 is a prime factor.
First, look for a factor. The most obvious would be 5, because the number ends in a five, so must be divisible by 5. 65/5 = 13, so the other factor will be 13. So 65 / \ 5 13 and since both 5 and 13 are prime numbers, the tree can't go on any further.
XIII
Multiples of 13