Question

Tyrese is looking for all the factors of 156. So far, Tyrese has divided 156 by all of the counting numbers from 1 to 13, listing those numbers that divide 156 and listing the corresponding quotients. Here is Tyrese's work so far (not listed, but goes 1, 2, 3, 4, 6, 12, 13) Should Tyrese keep checking to see if numbers larger than 13 divide 156, or can Tyrese stop dividing at this point? If so, why? What are all the factors of 156?

Answer 1

Explanation:

let's do a prime factor analysis :

156 ÷ 2 = 78

78 ÷ 2 = 39

39 ÷ 2 no

39 ÷ 3 = 13

13 ÷ 3 no

13 ÷ 5 no

13 ÷ 7 no

13 ÷ 11 no

13 ÷ 13 = 1 finished

therefore,

156 = 2×2×3×13

1 and 156 are default factors (1 and the number itself are factors for every number).

all the other factors are combinations of these prime factors :

2×2 = 4

2×3 = 6

2×2×3 = 12

2×13 = 26

2×2×13 = 52

3×13 = 39

2×3×13 = 78

so, no he should not stop there, he has to include also the quotients as factors, and overall find all the prime factor combinations.

all the factors are

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156