Q: What is the total or count of factors of the number 21,052,000?

 A: 96

How do I find the total factors of the number 21,052,000?

Step 1

Find the prime factorization of the number 21,052,000.

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

Factor Tree
21,052,000
Factor Arrows
210,526,000
Factor Arrows
25,263,000
Factor Arrows
22,631,500
Factor Arrows
21,315,750
Factor Arrows
2657,875
Factor Arrows
5131,575
Factor Arrows
526,315
Factor Arrows
55,263
Factor Arrows
19277

The prime factorization in exponential form is: 25 x 53 x 191 x 2771

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.

21,052,000 = 25 x 53 x 191 x 2771
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(21052000) = (5 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(21052000) = (6)(4)(2)(2)
Down Arrow
d(21052000) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 21,052,000 and how to find them.

Try the factor calculator.

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