Q: What is the total or count of factors of the number 186,213,350?

A: 48

How do I find the total factors of the number 186,213,350?

Step 1

Find the prime factorization of the number 186,213,350.

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

Factor Tree

	186,213,350

2		93,106,675

	5		18,621,335

		5		3,724,267

			29		128,423

				167		769

The prime factorization in exponential form is: 2¹ x 5² x 29¹ x 167¹ x 769¹

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.

186,213,350 = 2¹ x 5² x 29¹ x 167¹ x 769¹

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

d(186213350) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)

d(186213350) = (2)(3)(2)(2)(2)

d(186213350) = 48

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Take a look at the factors page to see the factors of 186,213,350 and how to find them.

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