Q: What is the total or count of factors of the number 4,967,424?

 A: 198

How do I find the total factors of the number 4,967,424?

Step 1

Find the prime factorization of the number 4,967,424.

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

Factor Tree
4,967,424
Factor Arrows
22,483,712
Factor Arrows
21,241,856
Factor Arrows
2620,928
Factor Arrows
2310,464
Factor Arrows
2155,232
Factor Arrows
277,616
Factor Arrows
238,808
Factor Arrows
219,404
Factor Arrows
29,702
Factor Arrows
24,851
Factor Arrows
31,617
Factor Arrows
3539
Factor Arrows
777
Factor Arrows
711

The prime factorization in exponential form is: 210 x 32 x 72 x 111

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.

4,967,424 = 210 x 32 x 72 x 111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(4967424) = (10 + 1)(2 + 1)(2 + 1)(1 + 1)
Down Arrow
d(4967424) = (11)(3)(3)(2)
Down Arrow
d(4967424) = 198

More numbers for you to try

Take a look at the factors page to see the factors of 4,967,424 and how to find them.

Try the factor calculator.

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