Q: What is the total or count of factors of the number 375,424?

 A: 32

How do I find the total factors of the number 375,424?

Step 1

Find the prime factorization of the number 375,424.

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

Factor Tree
375,424
Factor Arrows
2187,712
Factor Arrows
293,856
Factor Arrows
246,928
Factor Arrows
223,464
Factor Arrows
211,732
Factor Arrows
25,866
Factor Arrows
22,933
Factor Arrows
7419

The prime factorization in exponential form is: 27 x 71 x 4191

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.

375,424 = 27 x 71 x 4191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(375424) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(375424) = (8)(2)(2)
Down Arrow
d(375424) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 375,424 and how to find them.

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