Q: What is the total or count of factors of the number 109,089,260?

 A: 48

How do I find the total factors of the number 109,089,260?

Step 1

Find the prime factorization of the number 109,089,260.

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

Factor Tree
109,089,260
Factor Arrows
254,544,630
Factor Arrows
227,272,315
Factor Arrows
55,454,463
Factor Arrows
7779,209
Factor Arrows
1941,011

The prime factorization in exponential form is: 22 x 51 x 71 x 191 x 41,0111

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.

109,089,260 = 22 x 51 x 71 x 191 x 41,0111
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
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d(109089260) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(109089260) = (3)(2)(2)(2)(2)
Down Arrow
d(109089260) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 109,089,260 and how to find them.

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