Q: What is the total or count of factors of the number 397,210?

 A: 32

How do I find the total factors of the number 397,210?

Step 1

Find the prime factorization of the number 397,210.

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

Factor Tree
397,210
Factor Arrows
2198,605
Factor Arrows
539,721
Factor Arrows
113,611
Factor Arrows
23157

The prime factorization in exponential form is: 21 x 51 x 111 x 231 x 1571

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.

397,210 = 21 x 51 x 111 x 231 x 1571
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(397210) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(397210) = (2)(2)(2)(2)(2)
Down Arrow
d(397210) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 397,210 and how to find them.

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