math
posted by sam
WHAT IS THE PRIME FACTORIZATION OF 45? and what is the sum of the only two prime numbers that differ by one ? Thank you

Steve
45 = 3^2 5^1
2+3 = 5 
sam
Thank you , but could you explain the factorization of 45? Idont get it

Steve
The 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. 
sam
Igot it now. Thank you so much
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