Q: What is the total or count of factors of the number 401,720,410?

A: 64

How do I find the total factors of the number 401,720,410?

Step 1

Find the prime factorization of the number 401,720,410.

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

Factor Tree

	401,720,410

2		200,860,205

	5		40,172,041

		7		5,738,863

			13		441,451

				281		1,571

The prime factorization in exponential form is: 2¹ x 5¹ x 7¹ x 13¹ x 281¹ x 1,571¹

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.

401,720,410 = 2¹ x 5¹ x 7¹ x 13¹ x 281¹ x 1,571¹

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

d(401720410) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(401720410) = (2)(2)(2)(2)(2)(2)

d(401720410) = 64

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Take a look at the factors page to see the factors of 401,720,410 and how to find them.

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