Q: What is the total or count of factors of the number 616,420?

 A: 72

How do I find the total factors of the number 616,420?

Step 1

Find the prime factorization of the number 616,420.

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

Factor Tree
616,420
Factor Arrows
2308,210
Factor Arrows
2154,105
Factor Arrows
530,821
Factor Arrows
74,403
Factor Arrows
7629
Factor Arrows
1737

The prime factorization in exponential form is: 22 x 51 x 72 x 171 x 371

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.

616,420 = 22 x 51 x 72 x 171 x 371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(616420) = (2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(616420) = (3)(2)(3)(2)(2)
Down Arrow
d(616420) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 616,420 and how to find them.

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