Q: What is the total or count of factors of the number 602,064,320?

A: 224

How do I find the total factors of the number 602,064,320?

Step 1

Find the prime factorization of the number 602,064,320.

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

Factor Tree

	602,064,320

2		301,032,160

	2		150,516,080

		2		75,258,040

			2		37,629,020

				2		18,814,510

					2		9,407,255

						5		1,881,451

							11		171,041

								13		13,157

									59		223

The prime factorization in exponential form is: 2⁶ x 5¹ x 11¹ x 13¹ x 59¹ x 223¹

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.

602,064,320 = 2⁶ x 5¹ x 11¹ x 13¹ x 59¹ x 223¹

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

d(602064320) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(602064320) = (7)(2)(2)(2)(2)(2)

d(602064320) = 224

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Take a look at the factors page to see the factors of 602,064,320 and how to find them.

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