Question

The product of three whole numbers is 120 how many different possibilities are there for the three whole numbers

Answer 1

We can factor 120 into
2 * 2 * 2 * 3 * 5

I think there are nine different possibilities
1) 8 * 3 * 5
2) 4 * 2 * 15
3) 4 * 6 * 5
4) 4 * 10 * 3
5) 2 * 2 * 30
6) 2 * 3 * 20
7) 2 * 5 * 12
8) 2 * 6 * 10
9) 2 * 15 * 4

Answer 2

Solution:

It is given that,

Product of three Whole numbers = 120

Factorizing 120 into Prime Factors

120 = 2 ×2 ×2×3×5

Number of Possibilities

=Arrangement of 5 things which are numbers(2,2,2,3,5) when 3 of them are equal

= $\frac{5!}{3!}=\frac{5 \times 4 \times 3!}{3!}=5 \times 4 =20$