# SOLUTION: find the prime factorization of 702 please show all of your work.

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 Question 550622: find the prime factorization of 702 please show all of your work. Found 2 solutions by Alan3354, Edwin McCravy:Answer by Alan3354(30993)   (Show Source): You can put this solution on YOUR website!find the prime factorization of 702 please show all of your work. ------- It's an even number, so divide by 2. If the result is an odd number, then try 3. Divide by 3's until the result is not an integer, then try 5, 7 , 11, 13, etc. Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!```Below is a factor tree. You should know some of the smaller prime numbers: 2,3,5,7,11,13,17,19,23,29,31,37,41 702 / \ 351× 2 <-(prime) /\ 117× 3 <-(prime) /\ 39× 3 <-(prime) /\ (prime)-> 13× 3 <-(prime) I wrote 702 on the top line. Then I found the smallest prime that would divide evenly into 702. That was 2, So I broke 702 down to 351×2 on the second line. Then I found the smallest prime that would divide evenly into 351. That was 3, So I broke 351 down to 117×3 on the third line. Then I found the smallest prime that would divide evenly into 117. That was 3, So I broke 117 down to 39×3 on the fourth line. Then I found the smallest prime that would divide evenly into 39. That was 3, So I broke 39 down to 13×3 on the fifth line. Then I discovered that 13 was also prime, and so I knew that I was done with the tree. So I put down the product of all the primes from the top down and got: 702 = 2×3×3×3×13 and since 3 appears 3 times I write it simpler using an exponent of 3: 702 = 2×3³×13 Edwin```