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The number of divisors of $2100$ is ____.
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Answer: 36

$2100 = 7\times 3\times 2^2 \times 5^2$

Hence, total number of factors will be $= (1+1)\times (1+1)\times (2+1)\times (2+1) \\= 2 \times 2\times 3 \times 3 \\= 36$,

because any factor is obtained by multiplying the prime factors zero or more times. (one extra for zero)
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$2100 = 7 * 3 * 2^{2} * 5^{2}$

To calculate the total number of divisors, take each power in the prime factorization obtained, and:

Step 1: Increment the power.

$(1+1) (1+1) (2+1) (2+1)$

Step 2: Calculate the product of it:

$(1+1) * (1+1) * (2+1)* (2+1)$

Answer: 36

Answer:

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