Q: What is the total or count of factors of the number 305,384,112?

A: 240

How do I find the total factors of the number 305,384,112?

Step 1

Find the prime factorization of the number 305,384,112.

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

Factor Tree

	305,384,112

2		152,692,056

	2		76,346,028

		2		38,173,014

			2		19,086,507

				3		6,362,169

					3		2,120,723

						11		192,793

							19		10,147

								73		139

The prime factorization in exponential form is: 2⁴ x 3² x 11¹ x 19¹ x 73¹ x 139¹

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.

305,384,112 = 2⁴ x 3² x 11¹ x 19¹ x 73¹ x 139¹

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

d(305384112) = (4 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(305384112) = (5)(3)(2)(2)(2)(2)

d(305384112) = 240

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Take a look at the factors page to see the factors of 305,384,112 and how to find them.

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