Q: What is the total or count of factors of the number 45,144,855?

 A: 72

How do I find the total factors of the number 45,144,855?

Step 1

Find the prime factorization of the number 45,144,855.

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

Factor Tree
45,144,855
Factor Arrows
315,048,285
Factor Arrows
35,016,095
Factor Arrows
51,003,219
Factor Arrows
7143,317
Factor Arrows
197,543
Factor Arrows
19397

The prime factorization in exponential form is: 32 x 51 x 71 x 192 x 3971

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.

45,144,855 = 32 x 51 x 71 x 192 x 3971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(45144855) = (2 + 1)(1 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(45144855) = (3)(2)(2)(3)(2)
Down Arrow
d(45144855) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 45,144,855 and how to find them.

Try the factor calculator.

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