# math

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

• math -

45 = 3^2 5^1

2+3 = 5

• math -

Thank you , but could you explain the factorization of 45? Idont get it

• math -

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.

• math -

Igot it now. Thank you so much

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