Q: What is the total or count of factors of the number 537,375,864?

A: 128

How do I find the total factors of the number 537,375,864?

Step 1

Find the prime factorization of the number 537,375,864.

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

Factor Tree

	537,375,864

2		268,687,932

	2		134,343,966

		2		67,171,983

			3		22,390,661

				23		973,507

					37		26,311

						83		317

The prime factorization in exponential form is: 2³ x 3¹ x 23¹ x 37¹ x 83¹ x 317¹

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.

537,375,864 = 2³ x 3¹ x 23¹ x 37¹ x 83¹ x 317¹

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

d(537375864) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(537375864) = (4)(2)(2)(2)(2)(2)

d(537375864) = 128

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Take a look at the factors page to see the factors of 537,375,864 and how to find them.

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