Q: What is the total or count of factors of the number 254,424,210?

 A: 128

How do I find the total factors of the number 254,424,210?

Step 1

Find the prime factorization of the number 254,424,210.

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

Factor Tree
254,424,210
Factor Arrows
2127,212,105
Factor Arrows
342,404,035
Factor Arrows
58,480,807
Factor Arrows
17498,871
Factor Arrows
3713,483
Factor Arrows
97139

The prime factorization in exponential form is: 21 x 31 x 51 x 171 x 371 x 971 x 1391

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)(g + 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.

254,424,210 = 21 x 31 x 51 x 171 x 371 x 971 x 1391
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)(g + 1)
Down Arrow
d(254424210) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(254424210) = (2)(2)(2)(2)(2)(2)(2)
Down Arrow
d(254424210) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 254,424,210 and how to find them.

Try the factor calculator.

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