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You find the prime factorization by breaking the number down into other numbers that are prime. Start by breaking up 312 into 39 * 8. 39 breaks up into 3 * 13, and 8 breaks up into 4 * 2 which breaks up into 2 * 2. So the prime factorization of 312 is 3 * 13 * 2 * 2 * 2 or 
. When you multiply those together you'll get 312.