Q: What is the total or count of factors of the number 321,420,224?

A: 112

How do I find the total factors of the number 321,420,224?

Step 1

Find the prime factorization of the number 321,420,224.

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

Factor Tree

	321,420,224

2		160,710,112

	2		80,355,056

		2		40,177,528

			2		20,088,764

				2		10,044,382

					2		5,022,191

						17		295,423

							29		10,187

								61		167

The prime factorization in exponential form is: 2⁶ x 17¹ x 29¹ x 61¹ x 167¹

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.

321,420,224 = 2⁶ x 17¹ x 29¹ x 61¹ x 167¹

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

d(321420224) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(321420224) = (7)(2)(2)(2)(2)

d(321420224) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 321,420,224 and how to find them.

Try the factor calculator.

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