Question 139196: I'm having problems understanding prime factors. For example 675, how would you break that down ?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Test all of the possible prime factors. The upper limit of your list of trial divisors is the integer part of  . The calculator says that is about 25.98, so you only have to test prime divisors less than 25, namely 2, 3, 5, 7, 11, 13, 17, 19, and 23.
675 is odd, so 2 is NOT a factor.
6 + 7 + 5 = 18. 18 is divisible by 3, so 3 is a factor:
675/3 = 225
2 + 2 + 5 = 9. 9 is divisible by 3, so 3 is a factor:
225/3 = 75
7 + 5 = 12. 12 is divisible by 3, so 3 is a factor:
75/3 = 25
25 = 5 * 5 (By the way, we knew that 5 was a factor right from the beginning because 675 ends in 5, and anything that ends in 5 or 0 is divisible by 5)
In summary: 675 = 3 * 3 * 3 * 5 * 5
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