Q: What is the total or count of factors of the number 74,398,272?

 A: 112

How do I find the total factors of the number 74,398,272?

Step 1

Find the prime factorization of the number 74,398,272.

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

Factor Tree
74,398,272
Factor Arrows
237,199,136
Factor Arrows
218,599,568
Factor Arrows
29,299,784
Factor Arrows
24,649,892
Factor Arrows
22,324,946
Factor Arrows
21,162,473
Factor Arrows
3387,491
Factor Arrows
1329,807
Factor Arrows
41727

The prime factorization in exponential form is: 26 x 31 x 131 x 411 x 7271

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.

74,398,272 = 26 x 31 x 131 x 411 x 7271
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(74398272) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(74398272) = (7)(2)(2)(2)(2)
Down Arrow
d(74398272) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 74,398,272 and how to find them.

Try the factor calculator.

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