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CTET Paper I (Classes I to V) Nov 2012 Solved Paper

Question : 34 of 150

Marks: +1, -0

The sum of all the factors of 100 is

Solution:

Concept:

The sum of all factors of a number is found using its prime factorization and the formula for geometric series.

Explanation:

First, factor 100:

100 = 2^2 \times 5^2

For each prime factor, write the sum of its powers from

0

to the exponent.

Sum for

2

2^0 + 2^1 + 2^2 = 1 + 2 + 4 = 7

Sum for

5

5^0 + 5^1 + 5^2 = 1 + 5 + 25 = 31

Multiply these sums:

7 \times 31 = 217

Thus, the total sum of all factors of 100 is 217.

Answer:

217 (Option C)

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