Q: What is the total or count of factors of the number 362,196,064?

 A: 72

How do I find the total factors of the number 362,196,064?

Step 1

Find the prime factorization of the number 362,196,064.

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

Factor Tree
362,196,064
Factor Arrows
2181,098,032
Factor Arrows
290,549,016
Factor Arrows
245,274,508
Factor Arrows
222,637,254
Factor Arrows
211,318,627
Factor Arrows
31365,117
Factor Arrows
536,889
Factor Arrows
8383

The prime factorization in exponential form is: 25 x 311 x 531 x 832

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.

362,196,064 = 25 x 311 x 531 x 832
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(362196064) = (5 + 1)(1 + 1)(1 + 1)(2 + 1)
Down Arrow
d(362196064) = (6)(2)(2)(3)
Down Arrow
d(362196064) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 362,196,064 and how to find them.

Try the factor calculator.

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