Q: What is the total or count of factors of the number 401,720,410?

 A: 64

How do I find the total factors of the number 401,720,410?

Step 1

Find the prime factorization of the number 401,720,410.

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

Factor Tree
401,720,410
Factor Arrows
2200,860,205
Factor Arrows
540,172,041
Factor Arrows
75,738,863
Factor Arrows
13441,451
Factor Arrows
2811,571

The prime factorization in exponential form is: 21 x 51 x 71 x 131 x 2811 x 1,5711

Step 2

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

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

401,720,410 = 21 x 51 x 71 x 131 x 2811 x 1,5711
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(401720410) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(401720410) = (2)(2)(2)(2)(2)(2)
Down Arrow
d(401720410) = 64

More numbers for you to try

Take a look at the factors page to see the factors of 401,720,410 and how to find them.

Try the factor calculator.

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