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CTET Paper I (Classes I to V) Feb 2015 Solved Paper

Question : 59 of 150

Marks: +1, -0

The sum of all the positive factors of 96 is

Solution:

Concept:

Positive factors of a number are all divisors that divide it exactly, including 1 and the number itself.

Explanation:

First, find prime factorization of 96:

96 = 2^5 \times 3^1

Use the formula for sum of factors:

\frac{2^{6}-1}{2-1} \times \frac{3^{2}-1}{3-1} = \frac{64-1}{1} \times \frac{9-1}{2} = 63 \times 4 = 252

Alternatively, list all positive factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

Their sum is

1+2+3+4+6+8+12+16+24+32+48+96 = 252

Answer:

A. 252

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