Q: What is the total or count of factors of the number 78,438,140?

 A: 48

How do I find the total factors of the number 78,438,140?

Step 1

Find the prime factorization of the number 78,438,140.

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

Factor Tree
78,438,140
Factor Arrows
239,219,070
Factor Arrows
219,609,535
Factor Arrows
53,921,907
Factor Arrows
11356,537
Factor Arrows
596,043

The prime factorization in exponential form is: 22 x 51 x 111 x 591 x 6,0431

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.

78,438,140 = 22 x 51 x 111 x 591 x 6,0431
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(78438140) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(78438140) = (3)(2)(2)(2)(2)
Down Arrow
d(78438140) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 78,438,140 and how to find them.

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