Q: What is the total or count of factors of the number 625,408?

 A: 36

How do I find the total factors of the number 625,408?

Step 1

Find the prime factorization of the number 625,408.

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

Factor Tree
625,408
Factor Arrows
2312,704
Factor Arrows
2156,352
Factor Arrows
278,176
Factor Arrows
239,088
Factor Arrows
219,544
Factor Arrows
29,772
Factor Arrows
24,886
Factor Arrows
22,443
Factor Arrows
7349

The prime factorization in exponential form is: 28 x 71 x 3491

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

625,408 = 28 x 71 x 3491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(625408) = (8 + 1)(1 + 1)(1 + 1)
Down Arrow
d(625408) = (9)(2)(2)
Down Arrow
d(625408) = 36

More numbers for you to try

Take a look at the factors page to see the factors of 625,408 and how to find them.

Try the factor calculator.

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