Q: What is the total or count of factors of the number 64,423,546?

A: 48

How do I find the total factors of the number 64,423,546?

Step 1

Find the prime factorization of the number 64,423,546.

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

Factor Tree

	64,423,546

2		32,211,773

	11		2,928,343

		11		266,213

			41		6,493

				43		151

The prime factorization in exponential form is: 2¹ x 11² x 41¹ x 43¹ x 151¹

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.

64,423,546 = 2¹ x 11² x 41¹ x 43¹ x 151¹

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

d(64423546) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)

d(64423546) = (2)(3)(2)(2)(2)

d(64423546) = 48

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Take a look at the factors page to see the factors of 64,423,546 and how to find them.

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