Question

Which of the following numbers has the sum of the factors as twice itself?

• A. 48
• B. 28
• C. 54
• D. 36

Answer 1

The correct option is B 28

Let us write the factors of all the given numbers.

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
Sum of factors of 48 = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48
= 124

The factors of 28 are 1, 2, 4, 7, 14 and 28
Sum of factors of 28 = 1 + 2 + 4 + 7 + 14 + 28
= 56
56 = 2 × 28

The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54
Sum of factors of 54 = 1 + 2 + 3 + 6 + 9 + 18 + 27 + 54
= 120

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36
Sum of factors of 36 = 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36
= 91

Thus, the sum of the factors of 28 is twice the number.