Q: What is the total or count of factors of the number 21,435,750?

 A: 96

How do I find the total factors of the number 21,435,750?

Step 1

Find the prime factorization of the number 21,435,750.

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

Factor Tree
21,435,750
Factor Arrows
210,717,875
Factor Arrows
33,572,625
Factor Arrows
31,190,875
Factor Arrows
5238,175
Factor Arrows
547,635
Factor Arrows
59,527
Factor Arrows
71,361

The prime factorization in exponential form is: 21 x 32 x 53 x 71 x 1,3611

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.

21,435,750 = 21 x 32 x 53 x 71 x 1,3611
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(21435750) = (1 + 1)(2 + 1)(3 + 1)(1 + 1)(1 + 1)
Down Arrow
d(21435750) = (2)(3)(4)(2)(2)
Down Arrow
d(21435750) = 96

More numbers for you to try

Take a look at the factors page to see the factors of 21,435,750 and how to find them.

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