Q: What is the total or count of factors of the number 345,206,250?

 A: 216

How do I find the total factors of the number 345,206,250?

Step 1

Find the prime factorization of the number 345,206,250.

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

Factor Tree
345,206,250
Factor Arrows
2172,603,125
Factor Arrows
357,534,375
Factor Arrows
319,178,125
Factor Arrows
53,835,625
Factor Arrows
5767,125
Factor Arrows
5153,425
Factor Arrows
530,685
Factor Arrows
56,137
Factor Arrows
17361
Factor Arrows
1919

The prime factorization in exponential form is: 21 x 32 x 55 x 171 x 192

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.

345,206,250 = 21 x 32 x 55 x 171 x 192
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(345206250) = (1 + 1)(2 + 1)(5 + 1)(1 + 1)(2 + 1)
Down Arrow
d(345206250) = (2)(3)(6)(2)(3)
Down Arrow
d(345206250) = 216

More numbers for you to try

Take a look at the factors page to see the factors of 345,206,250 and how to find them.

Try the factor calculator.

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