Q: What is the total or count of factors of the number 106,224,160?

 A: 144

How do I find the total factors of the number 106,224,160?

Step 1

Find the prime factorization of the number 106,224,160.

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

Factor Tree
106,224,160
Factor Arrows
253,112,080
Factor Arrows
226,556,040
Factor Arrows
213,278,020
Factor Arrows
26,639,010
Factor Arrows
23,319,505
Factor Arrows
5663,901
Factor Arrows
794,843
Factor Arrows
713,549
Factor Arrows
17797

The prime factorization in exponential form is: 25 x 51 x 72 x 171 x 7971

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.

106,224,160 = 25 x 51 x 72 x 171 x 7971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(106224160) = (5 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(106224160) = (6)(2)(3)(2)(2)
Down Arrow
d(106224160) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 106,224,160 and how to find them.

Try the factor calculator.

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