Q: What is the total or count of factors of the number 105,305,512?

A: 64

How do I find the total factors of the number 105,305,512?

Step 1

Find the prime factorization of the number 105,305,512.

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

Factor Tree

	105,305,512

2		52,652,756

	2		26,326,378

		2		13,163,189

			13		1,012,553

				31		32,663

					89		367

The prime factorization in exponential form is: 2³ x 13¹ x 31¹ x 89¹ x 367¹

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.

105,305,512 = 2³ x 13¹ x 31¹ x 89¹ x 367¹

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

d(105305512) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(105305512) = (4)(2)(2)(2)(2)

d(105305512) = 64

More numbers for you to try

Take a look at the factors page to see the factors of 105,305,512 and how to find them.

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