Q: What is the total or count of factors of the number 540,054,144?

 A: 192

How do I find the total factors of the number 540,054,144?

Step 1

Find the prime factorization of the number 540,054,144.

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

Factor Tree
540,054,144
Factor Arrows
2270,027,072
Factor Arrows
2135,013,536
Factor Arrows
267,506,768
Factor Arrows
233,753,384
Factor Arrows
216,876,692
Factor Arrows
28,438,346
Factor Arrows
24,219,173
Factor Arrows
31,406,391
Factor Arrows
3468,797
Factor Arrows
766,971
Factor Arrows
193347

The prime factorization in exponential form is: 27 x 32 x 71 x 1931 x 3471

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.

540,054,144 = 27 x 32 x 71 x 1931 x 3471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(540054144) = (7 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(540054144) = (8)(3)(2)(2)(2)
Down Arrow
d(540054144) = 192

More numbers for you to try

Take a look at the factors page to see the factors of 540,054,144 and how to find them.

Try the factor calculator.

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