Q: What is the total or count of factors of the number 404,142,200?

 A: 288

How do I find the total factors of the number 404,142,200?

Step 1

Find the prime factorization of the number 404,142,200.

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

Factor Tree
404,142,200
Factor Arrows
2202,071,100
Factor Arrows
2101,035,550
Factor Arrows
250,517,775
Factor Arrows
510,103,555
Factor Arrows
52,020,711
Factor Arrows
7288,673
Factor Arrows
741,239
Factor Arrows
113,749
Factor Arrows
23163

The prime factorization in exponential form is: 23 x 52 x 72 x 111 x 231 x 1631

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.

404,142,200 = 23 x 52 x 72 x 111 x 231 x 1631
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(404142200) = (3 + 1)(2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(404142200) = (4)(3)(3)(2)(2)(2)
Down Arrow
d(404142200) = 288

More numbers for you to try

Take a look at the factors page to see the factors of 404,142,200 and how to find them.

Try the factor calculator.

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