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Find the total number of divisors for 3380

Question

Find the total number of divisors for 3380

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Solution

To find the total number of divisors for 3380, we first need to find the prime factorization of the number.

Step 1: Prime factorization of 3380 3380 = 2^2 * 5 * 13 * 13

Step 2: Find the total number of divisors The formula to find the total number of divisors is (a+1)(b+1)(c+1)... where a, b, c are the powers of the prime factors.

In this case, the powers of the prime factors are 2, 1, 1, and 1.

So, the total number of divisors is (2+1)(1+1)(1+1)(1+1) = 3 * 2 * 2 * 2 = 24

Therefore, 3380 has 24 divisors.

This problem has been solved

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Number of DivisorsGiven a number, find the number of divisors of that number.Input FormatFirst line of input contains T - number of test cases. Its followed by T lines, each containing a single number N.Output FormatFor each test case, print the number of divisors of N, separated by newline.Constraints30 points1 <= T <= 1001 <= N <= 10670 points1 <= T <= 1001 <= N <= 109ExampleInput581680892397158Output416328ExplanationSelf Explanatory

The number of positive divisors of 224 − 1 is

1/3

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