Wednesday, June 24, 2009

Practice problems for prime factorization

Find the prime factorizations of the following numbers.

a) 128
b) 129
c) 130

d) Find all the factors of 130.

Answers in the comments.

2 comments:

Prof. Hubbard said...

a) 128 = 2*64 2 is prime, 64 is not
64 = 8*8 not primes
8 = 2*4 2 is prime, 4 is not
4 = 2*2

128=2*8*8 becomes
128 = 2*2*2*2*2*2*2 = 2^7

b) 129 = 3*43 3 is prime and 43 is prime so we are done.
129 = 3*43

c) 130 = 13*10, 13 is prime and 10 is not
10 = 2*5 both are prime
130 = 2*5*13

Prof. Hubbard said...

For part d), let's use the fact we already know that 130 = 2 * 5 * 13. We always start the factor list with 1 and the original number.

1 and 130
2 and 65
(not 3)
(not 4)
5 and 26
(not 6, 7, 8 or 9)
10 and 13

So the whole list from lowest to highest is:
1, 2, 5, 10, 13, 26, 65 and 130.