Q: What is the total or count of factors of the number 462,646,626?

 A: 48

How do I find the total factors of the number 462,646,626?

Step 1

Find the prime factorization of the number 462,646,626.

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

Factor Tree
462,646,626
Factor Arrows
2231,323,313
Factor Arrows
377,107,771
Factor Arrows
135,931,367
Factor Arrows
13456,259
Factor Arrows
467977

The prime factorization in exponential form is: 21 x 31 x 132 x 4671 x 9771

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.

462,646,626 = 21 x 31 x 132 x 4671 x 9771
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(462646626) = (1 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(462646626) = (2)(2)(3)(2)(2)
Down Arrow
d(462646626) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 462,646,626 and how to find them.

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