Q: What is the total or count of factors of the number 350,642,544?

 A: 240

How do I find the total factors of the number 350,642,544?

Step 1

Find the prime factorization of the number 350,642,544.

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

Factor Tree
350,642,544
Factor Arrows
2175,321,272
Factor Arrows
287,660,636
Factor Arrows
243,830,318
Factor Arrows
221,915,159
Factor Arrows
37,305,053
Factor Arrows
71,043,579
Factor Arrows
1761,387
Factor Arrows
173,611
Factor Arrows
23157

The prime factorization in exponential form is: 24 x 31 x 71 x 172 x 231 x 1571

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.

350,642,544 = 24 x 31 x 71 x 172 x 231 x 1571
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(350642544) = (4 + 1)(1 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(350642544) = (5)(2)(2)(3)(2)(2)
Down Arrow
d(350642544) = 240

More numbers for you to try

Take a look at the factors page to see the factors of 350,642,544 and how to find them.

Try the factor calculator.

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