Q: What is the total or count of factors of the number 42,404,032?

 A: 112

How do I find the total factors of the number 42,404,032?

Step 1

Find the prime factorization of the number 42,404,032.

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

Factor Tree
42,404,032
Factor Arrows
221,202,016
Factor Arrows
210,601,008
Factor Arrows
25,300,504
Factor Arrows
22,650,252
Factor Arrows
21,325,126
Factor Arrows
2662,563
Factor Arrows
1160,233
Factor Arrows
292,077
Factor Arrows
3167

The prime factorization in exponential form is: 26 x 111 x 291 x 311 x 671

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.

42,404,032 = 26 x 111 x 291 x 311 x 671
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(42404032) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(42404032) = (7)(2)(2)(2)(2)
Down Arrow
d(42404032) = 112

More numbers for you to try

Take a look at the factors page to see the factors of 42,404,032 and how to find them.

Try the factor calculator.

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