Q: What is the total or count of factors of the number 2,814,624?

 A: 72

How do I find the total factors of the number 2,814,624?

Step 1

Find the prime factorization of the number 2,814,624.

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

Factor Tree
2,814,624
Factor Arrows
21,407,312
Factor Arrows
2703,656
Factor Arrows
2351,828
Factor Arrows
2175,914
Factor Arrows
287,957
Factor Arrows
329,319
Factor Arrows
39,773
Factor Arrows
29337

The prime factorization in exponential form is: 25 x 32 x 291 x 3371

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)

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.

2,814,624 = 25 x 32 x 291 x 3371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(2814624) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(2814624) = (6)(3)(2)(2)
Down Arrow
d(2814624) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 2,814,624 and how to find them.

Try the factor calculator.

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