Q: What is the total or count of factors of the number 251,152,152?

 A: 128

How do I find the total factors of the number 251,152,152?

Step 1

Find the prime factorization of the number 251,152,152.

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

Factor Tree
251,152,152
Factor Arrows
2125,576,076
Factor Arrows
262,788,038
Factor Arrows
231,394,019
Factor Arrows
310,464,673
Factor Arrows
17615,569
Factor Arrows
3716,637
Factor Arrows
127131

The prime factorization in exponential form is: 23 x 31 x 171 x 371 x 1271 x 1311

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.

251,152,152 = 23 x 31 x 171 x 371 x 1271 x 1311
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(251152152) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(251152152) = (4)(2)(2)(2)(2)(2)
Down Arrow
d(251152152) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 251,152,152 and how to find them.

Try the factor calculator.

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