Q: What is the total or count of factors of the number 803,968?

 A: 32

How do I find the total factors of the number 803,968?

Step 1

Find the prime factorization of the number 803,968.

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

Factor Tree
803,968
Factor Arrows
2401,984
Factor Arrows
2200,992
Factor Arrows
2100,496
Factor Arrows
250,248
Factor Arrows
225,124
Factor Arrows
212,562
Factor Arrows
26,281
Factor Arrows
11571

The prime factorization in exponential form is: 27 x 111 x 5711

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 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.

803,968 = 27 x 111 x 5711
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)
Down Arrow
d(803968) = (7 + 1)(1 + 1)(1 + 1)
Down Arrow
d(803968) = (8)(2)(2)
Down Arrow
d(803968) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 803,968 and how to find them.

Try the factor calculator.

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