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February 13, 2016
Posted by **sam ** on Monday, July 8, 2013 at 9:40am.

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**Steve**, Monday, July 8, 2013 at 9:51am45 = 3^2 5^1

2+3 = 5

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**sam**, Monday, July 8, 2013 at 10:13amThank you , but could you explain the factorization of 45? Idont get it

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**Steve**, Monday, July 8, 2013 at 10:38amThe easiest way to find the factors is to start with the smallest prime, and see whether it is a factor. Continue dividing successive primes until all you are left with is 1.

Is 2 a factor of 45? No.

How about he next prime (3)?

3 divides 45 twice, so 3^2 is included in the list.

45/3^2 = 5, so we keep going.

5 divides 5 once, so 5^1 is in the list.

5/5 = 1, so we are done.

The list of factors is 3^2 5^1

Consider 166600

166600/2 = 83300

83300/2 = 41650

41650/2 = 20825

2 does not divide 20825, so 2^3 is in the list

3 does not divide 20825

20825/5 = 4165

4165/5 = 833

5 does not divide 833, so 5^2 is in the list

833/7 = 119

119/7 = 17

7 does not divide 17, so 7^2 is in the list

17 is prime, so the final factorization is

2^3 5^2 7^2 17

As you can see, the method is quite simple, but very cumbersome for large numbers.

- math -
**sam**, Monday, July 8, 2013 at 10:55amIgot it now. Thank you so much