Q: What is the total or count of factors of the number 131,141,340?

 A: 144

How do I find the total factors of the number 131,141,340?

Step 1

Find the prime factorization of the number 131,141,340.

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

Factor Tree
131,141,340
Factor Arrows
265,570,670
Factor Arrows
232,785,335
Factor Arrows
310,928,445
Factor Arrows
33,642,815
Factor Arrows
5728,563
Factor Arrows
1166,233
Factor Arrows
107619

The prime factorization in exponential form is: 22 x 32 x 51 x 111 x 1071 x 6191

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)(f + 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.

131,141,340 = 22 x 32 x 51 x 111 x 1071 x 6191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(131141340) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(131141340) = (3)(3)(2)(2)(2)(2)
Down Arrow
d(131141340) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 131,141,340 and how to find them.

Try the factor calculator.

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