Q: What is the total or count of factors of the number 21,400,320?

 A: 72

How do I find the total factors of the number 21,400,320?

Step 1

Find the prime factorization of the number 21,400,320.

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

Factor Tree
21,400,320
Factor Arrows
210,700,160
Factor Arrows
25,350,080
Factor Arrows
22,675,040
Factor Arrows
21,337,520
Factor Arrows
2668,760
Factor Arrows
2334,380
Factor Arrows
2167,190
Factor Arrows
283,595
Factor Arrows
327,865
Factor Arrows
55,573

The prime factorization in exponential form is: 28 x 31 x 51 x 5,5731

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.

21,400,320 = 28 x 31 x 51 x 5,5731
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(21400320) = (8 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(21400320) = (9)(2)(2)(2)
Down Arrow
d(21400320) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 21,400,320 and how to find them.

Try the factor calculator.

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