Question 550622: find the prime factorization of 702 please show all of your work.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! find the prime factorization of 702 please show all of your work.
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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(20055)  (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
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