If x, y, and z are positive integers and 2 ∗ 3 ∗ 5 = 54,000, what is the value of x + y + z?

Question

answer  p

Answer 1

Factors of 54000=2⁴×3³×5³.

If x, y and z are the powers then x=4 and y=z=3.

Answer 2

You start by dividing 54000 from any number, 2, 3 , or 5. I'll start from dividing 54000 by 5, which is 10,800, and keep diving until you get a number that cannot be divided by 5. So 10800 / 5 = 2160. 2160 / 5 = 432. And 432 cannot be divided further by 5. So we have divided 54000 by five 3 times. So the first number will be 5^3  So now we move to another number like 3. 432 / 3 = 144. 144 / 3 = 48. 48 / 3 = 16. So now 3 doesn't go into 16 anymore, so the next number is 3^3. next is 2. 2^4 is 16.

So 2^4 x 3^3 x 5^3 = 54,000

And x = 4, y = 3, z = 3.

So x + y + z = 4 + 3 + 3 which 10.