Question

If the sum of common positive factors of 56 and 84 = 400 - 43 × _____, then the number which comes in blank space is:
1. 6
2. 8
3. 2
4. 3

Answer 1

Correct Answer - Option 2 : 8

Calculation

Let the number which comes in blank space be 'a'

Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56

Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

So common factors of 56 and 84 = 1, 2, 4, 7, 14, 28

The sum of the common factors = 1 + 2 + 4 + 7 + 14 + 28 = 56

As given, 56 = 400 - 43 × a

⇒ 43 × a = 400 - 56 = 344

⇒ a = 344 ÷ 43 = 8

∴ The required number is 8.