Q: What is the total or count of factors of the number 658,312?

 A: 32

How do I find the total factors of the number 658,312?

Step 1

Find the prime factorization of the number 658,312.

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

Factor Tree
658,312
Factor Arrows
2329,156
Factor Arrows
2164,578
Factor Arrows
282,289
Factor Arrows
194,331
Factor Arrows
6171

The prime factorization in exponential form is: 23 x 191 x 611 x 711

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.

658,312 = 23 x 191 x 611 x 711
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(658312) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(658312) = (4)(2)(2)(2)
Down Arrow
d(658312) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 658,312 and how to find them.

Try the factor calculator.

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