Question

Given M and N are whole numbers. Find the greatest value of the product M x N such that each of the following is true:

Answer 1

92

Explanation:

M is the prime number 23 (two factors are 1 and 23) and N is the square number 4 (factors are 1, 2, and 4). 23 x 4= 92

Answer 2

• 8 and 9

Explanation:

Let's assume all the factors are different.

Then the product of lowest 5 factors is:

• 2*3*5*7*9 > 98

If 2 of the factors are same and 3 are same, then the lowest ones:

• 2^3*3^2 = 72 < 98
• 3^3*2^2 = 108 > 98

As we see the only option is N = 2^3 = 8 and M = 3^2 = 9