Q: What is the total or count of factors of the number 162,282?

 A: 32

How do I find the total factors of the number 162,282?

Step 1

Find the prime factorization of the number 162,282.

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

Factor Tree
162,282
Factor Arrows
281,141
Factor Arrows
327,047
Factor Arrows
171,591
Factor Arrows
3743

The prime factorization in exponential form is: 21 x 31 x 171 x 371 x 431

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.

162,282 = 21 x 31 x 171 x 371 x 431
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(162282) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(162282) = (2)(2)(2)(2)(2)
Down Arrow
d(162282) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 162,282 and how to find them.

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