How do you find the prime factorization of 561?

Answer 1

Work your way through the Prime number posibilities. It's odd so there are no even factors. Add all the digits together (to get 12) and the result has a factor of 3 so 561 has a factor 3. Divide by that factor 3 to get 187. Try again for another factor 3 and there isn't one. The number 187 doesn't end in 5 (or 0) so 5 is not a factor. 7 doesn't divide exactly. 9 doesn't divide exactly. 11 does, so it is a factor. Divide by 11 to get 17 which is a prime number, so that's the finish. The factorization is 3x11x17