Find the total number of divisors for 3380
Question
Find the total number of divisors for 3380
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.
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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
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