Question

The sum of all the factors of 45000 which are exactly the multiples of 10 is:

• A. 152295
• B. 141960
• C. 600
• D. none of these

Answer 1

The correct option is B 141960

Since 45000 = 10 $\times$ 4500
Since the sum of all the factors of 45000 which are the multiples of 10 will be same as the sum of all the factors of 4500 multiplied by 10.
Now, 4500 = $2^2\times 3^2\times 5^3$
Therefore the sum of all the factors of
$4500=\frac{(2^3-1)\times (3^3-1)(5^4-1)}{(2-1)(3-1)(5-1)}=\frac{7\times 26\times 624}{1\times 2\times 4}=14196$
Hence the sum of all the products of 45000 which are the multiples of 10 = 10 $\times$ 14196 = 141960