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Question

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


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Solution

Step 1: Solve for factors of the given number

Factors of a number N can be represented as N=pa×qb×rc 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=32×5×11

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.

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.


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