Q: What is the total or count of factors of the number 71,465,200?

 A: 60

How do I find the total factors of the number 71,465,200?

Step 1

Find the prime factorization of the number 71,465,200.

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

Factor Tree
71,465,200
Factor Arrows
235,732,600
Factor Arrows
217,866,300
Factor Arrows
28,933,150
Factor Arrows
24,466,575
Factor Arrows
5893,315
Factor Arrows
5178,663
Factor Arrows
533,371

The prime factorization in exponential form is: 24 x 52 x 531 x 3,3711

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.

71,465,200 = 24 x 52 x 531 x 3,3711
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(71465200) = (4 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(71465200) = (5)(3)(2)(2)
Down Arrow
d(71465200) = 60

More numbers for you to try

Take a look at the factors page to see the factors of 71,465,200 and how to find them.

Try the factor calculator.

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