Q: What is the total or count of factors of the number 240,114,020?

A: 96

How do I find the total factors of the number 240,114,020?

Step 1

Find the prime factorization of the number 240,114,020.

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

Factor Tree

	240,114,020

2		120,057,010

	2		60,028,505

		5		12,005,701

			19		631,879

				23		27,473

					83		331

The prime factorization in exponential form is: 2² x 5¹ x 19¹ x 23¹ x 83¹ x 331¹

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.

240,114,020 = 2² x 5¹ x 19¹ x 23¹ x 83¹ x 331¹

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

d(240114020) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(240114020) = (3)(2)(2)(2)(2)(2)

d(240114020) = 96

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Take a look at the factors page to see the factors of 240,114,020 and how to find them.

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