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.
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Online notes for Math 15, Math for Liberal Arts taught in the Fall 2016 semester at Laney College by Prof. Hubbard.
2 comments:
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
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.
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