Q: What is the total or count of factors of the number 437,512,240?

A: 160

How do I find the total factors of the number 437,512,240?

Step 1

Find the prime factorization of the number 437,512,240.

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

Factor Tree

	437,512,240

2		218,756,120

	2		109,378,060

		2		54,689,030

			2		27,344,515

				5		5,468,903

					11		497,173

						19		26,167

							137		191

The prime factorization in exponential form is: 2⁴ x 5¹ x 11¹ x 19¹ x 137¹ x 191¹

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.

437,512,240 = 2⁴ x 5¹ x 11¹ x 19¹ x 137¹ x 191¹

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

d(437512240) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(437512240) = (5)(2)(2)(2)(2)(2)

d(437512240) = 160

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Take a look at the factors page to see the factors of 437,512,240 and how to find them.

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