Q: What is the total or count of factors of the number 401,240,224?

 A: 144

How do I find the total factors of the number 401,240,224?

Step 1

Find the prime factorization of the number 401,240,224.

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

Factor Tree
401,240,224
Factor Arrows
2200,620,112
Factor Arrows
2100,310,056
Factor Arrows
250,155,028
Factor Arrows
225,077,514
Factor Arrows
212,538,757
Factor Arrows
71,791,251
Factor Arrows
7255,893
Factor Arrows
1123,263
Factor Arrows
43541

The prime factorization in exponential form is: 25 x 72 x 111 x 431 x 5411

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.

401,240,224 = 25 x 72 x 111 x 431 x 5411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(401240224) = (5 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(401240224) = (6)(3)(2)(2)(2)
Down Arrow
d(401240224) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 401,240,224 and how to find them.

Try the factor calculator.

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