Q: What is the total or count of factors of the number 152,246,304?

 A: 144

How do I find the total factors of the number 152,246,304?

Step 1

Find the prime factorization of the number 152,246,304.

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

Factor Tree
152,246,304
Factor Arrows
276,123,152
Factor Arrows
238,061,576
Factor Arrows
219,030,788
Factor Arrows
29,515,394
Factor Arrows
24,757,697
Factor Arrows
31,585,899
Factor Arrows
3528,633
Factor Arrows
3176,211
Factor Arrows
358,737
Factor Arrows
319,579
Factor Arrows
72,797

The prime factorization in exponential form is: 25 x 35 x 71 x 2,7971

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.

152,246,304 = 25 x 35 x 71 x 2,7971
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(152246304) = (5 + 1)(5 + 1)(1 + 1)(1 + 1)
Down Arrow
d(152246304) = (6)(6)(2)(2)
Down Arrow
d(152246304) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 152,246,304 and how to find them.

Try the factor calculator.

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