Q: What is the total or count of factors of the number 40,070,784?

 A: 128

How do I find the total factors of the number 40,070,784?

Step 1

Find the prime factorization of the number 40,070,784.

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

Factor Tree
40,070,784
Factor Arrows
220,035,392
Factor Arrows
210,017,696
Factor Arrows
25,008,848
Factor Arrows
22,504,424
Factor Arrows
21,252,212
Factor Arrows
2626,106
Factor Arrows
2313,053
Factor Arrows
3104,351
Factor Arrows
138,027
Factor Arrows
23349

The prime factorization in exponential form is: 27 x 31 x 131 x 231 x 3491

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.

40,070,784 = 27 x 31 x 131 x 231 x 3491
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(40070784) = (7 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(40070784) = (8)(2)(2)(2)(2)
Down Arrow
d(40070784) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 40,070,784 and how to find them.

Try the factor calculator.

Explore more about the number 40,070,784:


Ask a Question