Q: What is the total or count of factors of the number 453,114,321?

 A: 32

How do I find the total factors of the number 453,114,321?

Step 1

Find the prime factorization of the number 453,114,321.

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

Factor Tree
453,114,321
Factor Arrows
3151,038,107
Factor Arrows
1113,730,737
Factor Arrows
31442,927
Factor Arrows
3711,971

The prime factorization in exponential form is: 31 x 111 x 311 x 371 x 11,9711

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.

453,114,321 = 31 x 111 x 311 x 371 x 11,9711
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
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d(453114321) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(453114321) = (2)(2)(2)(2)(2)
Down Arrow
d(453114321) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 453,114,321 and how to find them.

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