Q: What is the total or count of factors of the number 670,077,170?

A: 64

How do I find the total factors of the number 670,077,170?

Step 1

Find the prime factorization of the number 670,077,170.

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

Factor Tree

	670,077,170

2		335,038,585

	5		67,007,717

		7		9,572,531

			23		416,197

				43		9,679

The prime factorization in exponential form is: 2¹ x 5¹ x 7¹ x 23¹ x 43¹ x 9,679¹

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.

670,077,170 = 2¹ x 5¹ x 7¹ x 23¹ x 43¹ x 9,679¹

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

d(670077170) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(670077170) = (2)(2)(2)(2)(2)(2)

d(670077170) = 64

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Take a look at the factors page to see the factors of 670,077,170 and how to find them.

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