Question

The sum of all the positive divisors less than $250$ of the number $484$ is

• A. 931
• B. 445
• C. 447
• D. $none\, of\, these$

Answer 1

Answer: (C)

447

Answer 2

$484 = 2^2 \times 11^2$ Sum of all positive divisors $=\left(\frac{2^{3}-1}{2-1}\right)\left(\frac{11^{3}-1}{11-1}\right)$ $=\frac{7}{1}\times\frac{1330}{10}=931$ $\because$ There is only one divisor of $484$ which is greater than $250$ So, sum of all divisors less than $250 = 931- 484 = 447$