Q: What is the total or count of factors of the number 141,530,240?

 A: 128

How do I find the total factors of the number 141,530,240?

Step 1

Find the prime factorization of the number 141,530,240.

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

Factor Tree
141,530,240
Factor Arrows
270,765,120
Factor Arrows
235,382,560
Factor Arrows
217,691,280
Factor Arrows
28,845,640
Factor Arrows
24,422,820
Factor Arrows
22,211,410
Factor Arrows
21,105,705
Factor Arrows
5221,141
Factor Arrows
1911,639
Factor Arrows
103113

The prime factorization in exponential form is: 27 x 51 x 191 x 1031 x 1131

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.

141,530,240 = 27 x 51 x 191 x 1031 x 1131
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(141530240) = (7 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(141530240) = (8)(2)(2)(2)(2)
Down Arrow
d(141530240) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 141,530,240 and how to find them.

Try the factor calculator.

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