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Prime Factorization Prime Numbers A Prime Number is a whole number, greater than 1, that can be evenly divided only by 1 or itself. Factors "Factors" are the numbers you multiply together to get another number: Prime Factorization "Prime Factorization" is finding which prime numbers you need to multiply together to get the original number. Why? A prime number can only be divided by 1 or itself, so it cannot be factored any further! Every other number can be broken down into prime number factors. So, in a way, the prime numbers are the building blocks of all other numbers. A Factor Tree Makes Factoring Easy An easy way to factor a number is by making a factor tree. To make a tree, simply start with the number you want to factor. From there, make branches of factors numbers that multiply to give you the original number. Next, take each of those numbers and break those down into more factors. Continue until all the remaining numbers are prime numbers and cannot be factored anymore. Original Number Factors of 36 Factors of 9 and 4 So the factors of 36 are 2 · 2 · 3 · 3 or 22 · 32 Please note: You did not have to choose 9 and 4 as the first two "branches" of the tree. You can pick any two numbers that multiply to make 36. Other possibilities are 6 & 6, 3 & 12, and 2 & 18.