Q: What is the total or count of factors of the number 221,312,100?

A: 144

How do I find the total factors of the number 221,312,100?

Step 1

Find the prime factorization of the number 221,312,100.

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

Factor Tree

	221,312,100

2		110,656,050

	2		55,328,025

		3		18,442,675

			5		3,688,535

				5		737,707

					31		23,797

						53		449

The prime factorization in exponential form is: 2² x 3¹ x 5² x 31¹ x 53¹ x 449¹

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)(f + 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.

221,312,100 = 2² x 3¹ x 5² x 31¹ x 53¹ x 449¹

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

d(221312100) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)

d(221312100) = (3)(2)(3)(2)(2)(2)

d(221312100) = 144

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Take a look at the factors page to see the factors of 221,312,100 and how to find them.

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