Q: What is the total or count of factors of the number 194,141,640?

 A: 128

How do I find the total factors of the number 194,141,640?

Step 1

Find the prime factorization of the number 194,141,640.

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

Factor Tree
194,141,640
Factor Arrows
297,070,820
Factor Arrows
248,535,410
Factor Arrows
224,267,705
Factor Arrows
38,089,235
Factor Arrows
51,617,847
Factor Arrows
7231,121
Factor Arrows
1121,011

The prime factorization in exponential form is: 23 x 31 x 51 x 71 x 111 x 21,0111

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.

194,141,640 = 23 x 31 x 51 x 71 x 111 x 21,0111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(194141640) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(194141640) = (4)(2)(2)(2)(2)(2)
Down Arrow
d(194141640) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 194,141,640 and how to find them.

Try the factor calculator.

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