Q: What is the total or count of factors of the number 130,772,322?

A: 48

How do I find the total factors of the number 130,772,322?

Step 1

Find the prime factorization of the number 130,772,322.

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

Factor Tree

	130,772,322

2		65,386,161

	3		21,795,387

		3		7,265,129

			31		234,359

				131		1,789

The prime factorization in exponential form is: 2¹ x 3² x 31¹ x 131¹ x 1,789¹

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.

130,772,322 = 2¹ x 3² x 31¹ x 131¹ x 1,789¹

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

d(130772322) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)

d(130772322) = (2)(3)(2)(2)(2)

d(130772322) = 48

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Take a look at the factors page to see the factors of 130,772,322 and how to find them.

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