Q: What is the total or count of factors of the number 603,411,614?

A: 32

How do I find the total factors of the number 603,411,614?

Step 1

Find the prime factorization of the number 603,411,614.

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

Factor Tree

	603,411,614

2		301,705,807

	13		23,208,139

		19		1,221,481

			37		33,013

The prime factorization in exponential form is: 2¹ x 13¹ x 19¹ x 37¹ x 33,013¹

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.

603,411,614 = 2¹ x 13¹ x 19¹ x 37¹ x 33,013¹

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

d(603411614) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(603411614) = (2)(2)(2)(2)(2)

d(603411614) = 32

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Take a look at the factors page to see the factors of 603,411,614 and how to find them.

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