Q: What is the total or count of factors of the number 443,261,250?

 A: 180

How do I find the total factors of the number 443,261,250?

Step 1

Find the prime factorization of the number 443,261,250.

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

Factor Tree
443,261,250
Factor Arrows
2221,630,625
Factor Arrows
373,876,875
Factor Arrows
324,625,625
Factor Arrows
54,925,125
Factor Arrows
5985,025
Factor Arrows
5197,005
Factor Arrows
539,401
Factor Arrows
311,271
Factor Arrows
3141

The prime factorization in exponential form is: 21 x 32 x 54 x 312 x 411

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.

443,261,250 = 21 x 32 x 54 x 312 x 411
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(443261250) = (1 + 1)(2 + 1)(4 + 1)(2 + 1)(1 + 1)
Down Arrow
d(443261250) = (2)(3)(5)(3)(2)
Down Arrow
d(443261250) = 180

More numbers for you to try

Take a look at the factors page to see the factors of 443,261,250 and how to find them.

Try the factor calculator.

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