Q: What is the total or count of factors of the number 224,150,440?

 A: 128

How do I find the total factors of the number 224,150,440?

Step 1

Find the prime factorization of the number 224,150,440.

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

Factor Tree
224,150,440
Factor Arrows
2112,075,220
Factor Arrows
256,037,610
Factor Arrows
228,018,805
Factor Arrows
55,603,761
Factor Arrows
17329,633
Factor Arrows
378,909
Factor Arrows
59151

The prime factorization in exponential form is: 23 x 51 x 171 x 371 x 591 x 1511

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.

224,150,440 = 23 x 51 x 171 x 371 x 591 x 1511
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(224150440) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(224150440) = (4)(2)(2)(2)(2)(2)
Down Arrow
d(224150440) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 224,150,440 and how to find them.

Try the factor calculator.

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