Q: What is the total or count of factors of the number 102,323,250?

 A: 160

How do I find the total factors of the number 102,323,250?

Step 1

Find the prime factorization of the number 102,323,250.

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

Factor Tree
102,323,250
Factor Arrows
251,161,625
Factor Arrows
317,053,875
Factor Arrows
35,684,625
Factor Arrows
31,894,875
Factor Arrows
3631,625
Factor Arrows
5126,325
Factor Arrows
525,265
Factor Arrows
55,053
Factor Arrows
31163

The prime factorization in exponential form is: 21 x 34 x 53 x 311 x 1631

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.

102,323,250 = 21 x 34 x 53 x 311 x 1631
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(102323250) = (1 + 1)(4 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(102323250) = (2)(5)(4)(2)(2)
Down Arrow
d(102323250) = 160

More numbers for you to try

Take a look at the factors page to see the factors of 102,323,250 and how to find them.

Try the factor calculator.

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