Q: What is the total or count of factors of the number 15,301,440?

 A: 448

How do I find the total factors of the number 15,301,440?

Step 1

Find the prime factorization of the number 15,301,440.

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

Factor Tree
15,301,440
Factor Arrows
27,650,720
Factor Arrows
23,825,360
Factor Arrows
21,912,680
Factor Arrows
2956,340
Factor Arrows
2478,170
Factor Arrows
2239,085
Factor Arrows
379,695
Factor Arrows
326,565
Factor Arrows
38,855
Factor Arrows
51,771
Factor Arrows
7253
Factor Arrows
1123

The prime factorization in exponential form is: 26 x 33 x 51 x 71 x 111 x 231

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)(f + 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.

15,301,440 = 26 x 33 x 51 x 71 x 111 x 231
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(15301440) = (6 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(15301440) = (7)(4)(2)(2)(2)(2)
Down Arrow
d(15301440) = 448

More numbers for you to try

Take a look at the factors page to see the factors of 15,301,440 and how to find them.

Try the factor calculator.

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