Q: What is the total or count of factors of the number 45,616,648?

 A: 96

How do I find the total factors of the number 45,616,648?

Step 1

Find the prime factorization of the number 45,616,648.

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

Factor Tree
45,616,648
Factor Arrows
222,808,324
Factor Arrows
211,404,162
Factor Arrows
25,702,081
Factor Arrows
7814,583
Factor Arrows
7116,369
Factor Arrows
1110,579
Factor Arrows
71149

The prime factorization in exponential form is: 23 x 72 x 111 x 711 x 1491

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.

45,616,648 = 23 x 72 x 111 x 711 x 1491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(45616648) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(45616648) = (4)(3)(2)(2)(2)
Down Arrow
d(45616648) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 45,616,648 and how to find them.

Try the factor calculator.

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