Q: What is the total or count of factors of the number 413,105,231?

A: 48

How do I find the total factors of the number 413,105,231?

Step 1

Find the prime factorization of the number 413,105,231.

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

Factor Tree

	413,105,231

7		59,015,033

	7		8,430,719

		11		766,429

			23		33,323

				47		709

The prime factorization in exponential form is: 7² x 11¹ x 23¹ x 47¹ x 709¹

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.

413,105,231 = 7² x 11¹ x 23¹ x 47¹ x 709¹

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

d(413105231) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(413105231) = (3)(2)(2)(2)(2)

d(413105231) = 48

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Take a look at the factors page to see the factors of 413,105,231 and how to find them.

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