Q: What is the total or count of factors of the number 562,014,810?

 A: 144

How do I find the total factors of the number 562,014,810?

Step 1

Find the prime factorization of the number 562,014,810.

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

Factor Tree
562,014,810
Factor Arrows
2281,007,405
Factor Arrows
393,669,135
Factor Arrows
331,223,045
Factor Arrows
56,244,609
Factor Arrows
7892,087
Factor Arrows
7127,441
Factor Arrows
314,111

The prime factorization in exponential form is: 21 x 32 x 51 x 72 x 311 x 4,1111

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.

562,014,810 = 21 x 32 x 51 x 72 x 311 x 4,1111
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(562014810) = (1 + 1)(2 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(562014810) = (2)(3)(2)(3)(2)(2)
Down Arrow
d(562014810) = 144

More numbers for you to try

Take a look at the factors page to see the factors of 562,014,810 and how to find them.

Try the factor calculator.

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