Q: What is the total or count of factors of the number 100,120,032?

 A: 144

How do I find the total factors of the number 100,120,032?

Step 1

Find the prime factorization of the number 100,120,032.

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

Factor Tree
100,120,032
Factor Arrows
250,060,016
Factor Arrows
225,030,008
Factor Arrows
212,515,004
Factor Arrows
26,257,502
Factor Arrows
23,128,751
Factor Arrows
31,042,917
Factor Arrows
3347,639
Factor Arrows
418,479
Factor Arrows
61139

The prime factorization in exponential form is: 25 x 32 x 411 x 611 x 1391

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)

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.

100,120,032 = 25 x 32 x 411 x 611 x 1391
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(100120032) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(100120032) = (6)(3)(2)(2)(2)
Down Arrow
d(100120032) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 100,120,032 and how to find them.

Try the factor calculator.

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