Q: What is the total or count of factors of the number 978,692?

A: 48

How do I find the total factors of the number 978,692?

Step 1

Find the prime factorization of the number 978,692.

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

Factor Tree

	978,692

2		489,346

	2		244,673

		11		22,243

			13		1,711

				29		59

The prime factorization in exponential form is: 2² x 11¹ x 13¹ x 29¹ x 59¹

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.

978,692 = 2² x 11¹ x 13¹ x 29¹ x 59¹

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

d(978692) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(978692) = (3)(2)(2)(2)(2)

d(978692) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 978,692 and how to find them.

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