Q: What is the total or count of factors of the number 313,123,306?

A: 32

How do I find the total factors of the number 313,123,306?

Step 1

Find the prime factorization of the number 313,123,306.

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

Factor Tree

	313,123,306

2		156,561,653

	17		9,209,509

		19		484,711

			47		10,313

The prime factorization in exponential form is: 2¹ x 17¹ x 19¹ x 47¹ x 10,313¹

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.

313,123,306 = 2¹ x 17¹ x 19¹ x 47¹ x 10,313¹

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)

d(313123306) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(313123306) = (2)(2)(2)(2)(2)

d(313123306) = 32

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Take a look at the factors page to see the factors of 313,123,306 and how to find them.

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