Q: What is the total or count of factors of the number 152,213,040?

 A: 160

How do I find the total factors of the number 152,213,040?

Step 1

Find the prime factorization of the number 152,213,040.

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

Factor Tree
152,213,040
Factor Arrows
276,106,520
Factor Arrows
238,053,260
Factor Arrows
219,026,630
Factor Arrows
29,513,315
Factor Arrows
33,171,105
Factor Arrows
31,057,035
Factor Arrows
3352,345
Factor Arrows
570,469
Factor Arrows
710,067

The prime factorization in exponential form is: 24 x 33 x 51 x 71 x 10,0671

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.

152,213,040 = 24 x 33 x 51 x 71 x 10,0671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(152213040) = (4 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(152213040) = (5)(4)(2)(2)(2)
Down Arrow
d(152213040) = 160

More numbers for you to try

Take a look at the factors page to see the factors of 152,213,040 and how to find them.

Try the factor calculator.

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