Q: What is the total or count of factors of the number 34,828,160?

 A: 32

How do I find the total factors of the number 34,828,160?

Step 1

Find the prime factorization of the number 34,828,160.

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

Factor Tree
34,828,160
Factor Arrows
217,414,080
Factor Arrows
28,707,040
Factor Arrows
24,353,520
Factor Arrows
22,176,760
Factor Arrows
21,088,380
Factor Arrows
2544,190
Factor Arrows
2272,095
Factor Arrows
554,419

The prime factorization in exponential form is: 27 x 51 x 54,4191

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

34,828,160 = 27 x 51 x 54,4191
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(34828160) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(34828160) = (8)(2)(2)
Down Arrow
d(34828160) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 34,828,160 and how to find them.

Try the factor calculator.

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