Q: What is the total or count of factors of the number 653,670?

 A: 48

How do I find the total factors of the number 653,670?

Step 1

Find the prime factorization of the number 653,670.

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

Factor Tree
653,670
Factor Arrows
2326,835
Factor Arrows
3108,945
Factor Arrows
336,315
Factor Arrows
312,105
Factor Arrows
34,035
Factor Arrows
31,345
Factor Arrows
5269

The prime factorization in exponential form is: 21 x 35 x 51 x 2691

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.

653,670 = 21 x 35 x 51 x 2691
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(653670) = (1 + 1)(5 + 1)(1 + 1)(1 + 1)
Down Arrow
d(653670) = (2)(6)(2)(2)
Down Arrow
d(653670) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 653,670 and how to find them.

Try the factor calculator.

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