Q: What is the total or count of factors of the number 142,501,140?

 A: 288

How do I find the total factors of the number 142,501,140?

Step 1

Find the prime factorization of the number 142,501,140.

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

Factor Tree
142,501,140
Factor Arrows
271,250,570
Factor Arrows
235,625,285
Factor Arrows
311,875,095
Factor Arrows
33,958,365
Factor Arrows
31,319,455
Factor Arrows
5263,891
Factor Arrows
1715,523
Factor Arrows
19817
Factor Arrows
1943

The prime factorization in exponential form is: 22 x 33 x 51 x 171 x 192 x 431

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.

142,501,140 = 22 x 33 x 51 x 171 x 192 x 431
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(142501140) = (2 + 1)(3 + 1)(1 + 1)(1 + 1)(2 + 1)(1 + 1)
Down Arrow
d(142501140) = (3)(4)(2)(2)(3)(2)
Down Arrow
d(142501140) = 288

More numbers for you to try

Take a look at the factors page to see the factors of 142,501,140 and how to find them.

Try the factor calculator.

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