Q: What is the total or count of factors of the number 652,214,640?

 A: 320

How do I find the total factors of the number 652,214,640?

Step 1

Find the prime factorization of the number 652,214,640.

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

Factor Tree
652,214,640
Factor Arrows
2326,107,320
Factor Arrows
2163,053,660
Factor Arrows
281,526,830
Factor Arrows
240,763,415
Factor Arrows
313,587,805
Factor Arrows
52,717,561
Factor Arrows
7388,223
Factor Arrows
1135,293
Factor Arrows
291,217

The prime factorization in exponential form is: 24 x 31 x 51 x 71 x 111 x 291 x 1,2171

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)(g + 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.

652,214,640 = 24 x 31 x 51 x 71 x 111 x 291 x 1,2171
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)(g + 1)
Down Arrow
d(652214640) = (4 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(652214640) = (5)(2)(2)(2)(2)(2)(2)
Down Arrow
d(652214640) = 320

More numbers for you to try

Take a look at the factors page to see the factors of 652,214,640 and how to find them.

Try the factor calculator.

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