Question

How many triples of three positive integers have a product of 16?

Answer 1

There are 15 possible triples of three positive integers whose product is 16.

According to this question, we must find the quantity of all possible triples such that they have a product of 16. By factor decomposition, we have that 16 is equal to the following product of prime numbers:

$16 = 2^{4}$

There are the following triples considering order of factors:

(i) $\{16, 1, 1\}$, (ii) $\{1, 16, 1\}$, (iii) $\{1, 1, 16\}$, (iv) $\{2, 8, 1\}$, (v) $\{8, 2, 1\}$, (vi) $\{8, 1, 2\}$, (vii) $\{2, 1, 8\}$, (viii) $\{1, 2, 8\}$, (ix) $\{1, 8, 2\}$, (x) $\{1,4,4\}$, (xi) $\{4, 1, 4\}$, (xii) $\{4,4,1\}$, (xiii) $\{2,2,4\}$, (xiv) $\{2, 4, 2\}$, (xv) $\{4,2,2\}$

There are 15 possible triples of three positive integers whose product is 16.

We kindly invite to check this question on factor decomposition: brainly.com/question/2250220