Question

For $495$ find the sum of all factors less than $250$.

Answer 1

Step 1: Solve for factors of the given number

Factors of a number $N$ can be represented as $N=p^a\times q^b\times r^c$ where, $p$, $q$ and $r$ are prime factors of the number $N$ and $a$, $b$ and $c$ are non-negative exponents.

Given, $N$ is $495$.

$495=3^2\times 5\times 11$

$\therefore$The factors of $495$ are $1,3,5,9,11,15,33,45,55,99,165$ and $495$.

Step 2: Solve for sum of factors

Factors of $495$ less than $250$ are $1,3,5,9,11,15,33,45,55,99$ and $165$.

$\therefore$sum of all factors of $495$ that are less than $250$$=$$1+3+5+9+11+15+33+45+55+99+165=441$.

Hence, sum of all factors of $495$ that are less than $250$ is $441$.