Q: What is the total or count of factors of the number 701,408,730?

A: 128

How do I find the total factors of the number 701,408,730?

Step 1

Find the prime factorization of the number 701,408,730.

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

Factor Tree

	701,408,730

2		350,704,365

	3		116,901,455

		5		23,380,291

			11		2,125,481

				41		51,841

					47		1,103

The prime factorization in exponential form is: 2¹ x 3¹ x 5¹ x 11¹ x 41¹ x 47¹ x 1,103¹

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)(g + 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.

701,408,730 = 2¹ x 3¹ x 5¹ x 11¹ x 41¹ x 47¹ x 1,103¹

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

d(701408730) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(701408730) = (2)(2)(2)(2)(2)(2)(2)

d(701408730) = 128

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Take a look at the factors page to see the factors of 701,408,730 and how to find them.

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