Q: What is the total or count of factors of the number 102,441,021?

 A: 32

How do I find the total factors of the number 102,441,021?

Step 1

Find the prime factorization of the number 102,441,021.

Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.

Factor Tree
102,441,021
Factor Arrows
334,147,007
Factor Arrows
291,177,483
Factor Arrows
6119,303
Factor Arrows
97199

The prime factorization in exponential form is: 31 x 291 x 611 x 971 x 1991

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

102,441,021 = 31 x 291 x 611 x 971 x 1991
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(102441021) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(102441021) = (2)(2)(2)(2)(2)
Down Arrow
d(102441021) = 32

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Take a look at the factors page to see the factors of 102,441,021 and how to find them.

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