CTET Paper I (Classes I to V) Sep 2014 Solved Paper

Concept:To find the sum of all positive factors of a number, first express it as a product of primes. Then, for each prime power, add the prime raised to all powers from 0 to its exponent. Multiply these sums together.Explanation:First, factorize 210 into its prime factors: $210 = 2 \times 3 \times 5 \times 7$. Each prime appears only once (exponent 1).The sum of factors is given by: $(2^0 + 2^1) \times (3^0 + 3^1) \times (5^0 + 5^1) \times (7^0 + 7^1)$.Compute each sum: $1 + 2 = 3$, $1 + 3 = 4$, $1 + 5 = 6$, $1 + 7 = 8$.Multiply them: $3 \times 4 = 12$, $12 \times 6 = 72$, $72 \times 8 = 576$.Thus, the sum of all positive factors of 210 is 576.Answer:Option A: 576.