Q: What is the total or count of factors of the number 132,442,240?

 A: 256

How do I find the total factors of the number 132,442,240?

Step 1

Find the prime factorization of the number 132,442,240.

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

Factor Tree
132,442,240
Factor Arrows
266,221,120
Factor Arrows
233,110,560
Factor Arrows
216,555,280
Factor Arrows
28,277,640
Factor Arrows
24,138,820
Factor Arrows
22,069,410
Factor Arrows
21,034,705
Factor Arrows
5206,941
Factor Arrows
729,563
Factor Arrows
171,739
Factor Arrows
3747

The prime factorization in exponential form is: 27 x 51 x 71 x 171 x 371 x 471

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.

132,442,240 = 27 x 51 x 71 x 171 x 371 x 471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(132442240) = (7 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(132442240) = (8)(2)(2)(2)(2)(2)
Down Arrow
d(132442240) = 256

More numbers for you to try

Take a look at the factors page to see the factors of 132,442,240 and how to find them.

Try the factor calculator.

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