Q: What is the total or count of factors of the number 1,038,700?

 A: 72

How do I find the total factors of the number 1,038,700?

Step 1

Find the prime factorization of the number 1,038,700.

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

Factor Tree
1,038,700
Factor Arrows
2519,350
Factor Arrows
2259,675
Factor Arrows
551,935
Factor Arrows
510,387
Factor Arrows
13799
Factor Arrows
1747

The prime factorization in exponential form is: 22 x 52 x 131 x 171 x 471

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.

1,038,700 = 22 x 52 x 131 x 171 x 471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(1038700) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(1038700) = (3)(3)(2)(2)(2)
Down Arrow
d(1038700) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 1,038,700 and how to find them.

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