Q: What is the total or count of factors of the number 215,454,464?

 A: 72

How do I find the total factors of the number 215,454,464?

Step 1

Find the prime factorization of the number 215,454,464.

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

Factor Tree
215,454,464
Factor Arrows
2107,727,232
Factor Arrows
253,863,616
Factor Arrows
226,931,808
Factor Arrows
213,465,904
Factor Arrows
26,732,952
Factor Arrows
23,366,476
Factor Arrows
21,683,238
Factor Arrows
2841,619
Factor Arrows
1749,507
Factor Arrows
311,597

The prime factorization in exponential form is: 28 x 171 x 311 x 1,5971

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)

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.

215,454,464 = 28 x 171 x 311 x 1,5971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(215454464) = (8 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(215454464) = (9)(2)(2)(2)
Down Arrow
d(215454464) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 215,454,464 and how to find them.

Try the factor calculator.

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