Q: What is the total or count of factors of the number 350,422,254?

A: 128

How do I find the total factors of the number 350,422,254?

Step 1

Find the prime factorization of the number 350,422,254.

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

Factor Tree

	350,422,254

2		175,211,127

	3		58,403,709

		3		19,467,903

			3		6,489,301

				7		927,043

					13		71,311

						29		2,459

The prime factorization in exponential form is: 2¹ x 3³ x 7¹ x 13¹ x 29¹ x 2,459¹

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.

350,422,254 = 2¹ x 3³ x 7¹ x 13¹ x 29¹ x 2,459¹

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

d(350422254) = (1 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(350422254) = (2)(4)(2)(2)(2)(2)

d(350422254) = 128

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Take a look at the factors page to see the factors of 350,422,254 and how to find them.

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