Q: What is the total or count of factors of the number 554,086,346?

A: 48

How do I find the total factors of the number 554,086,346?

Step 1

Find the prime factorization of the number 554,086,346.

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

Factor Tree

	554,086,346

2		277,043,173

	11		25,185,743

		11		2,289,613

			59		38,807

				151		257

The prime factorization in exponential form is: 2¹ x 11² x 59¹ x 151¹ x 257¹

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.

554,086,346 = 2¹ x 11² x 59¹ x 151¹ x 257¹

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

d(554086346) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)

d(554086346) = (2)(3)(2)(2)(2)

d(554086346) = 48

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Take a look at the factors page to see the factors of 554,086,346 and how to find them.

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