Q: What is the total or count of factors of the number 340,000,400?

 A: 60

How do I find the total factors of the number 340,000,400?

Step 1

Find the prime factorization of the number 340,000,400.

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

Factor Tree
340,000,400
Factor Arrows
2170,000,200
Factor Arrows
285,000,100
Factor Arrows
242,500,050
Factor Arrows
221,250,025
Factor Arrows
54,250,005
Factor Arrows
5850,001
Factor Arrows
3722,973

The prime factorization in exponential form is: 24 x 52 x 371 x 22,9731

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)

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.

340,000,400 = 24 x 52 x 371 x 22,9731
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(340000400) = (4 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(340000400) = (5)(3)(2)(2)
Down Arrow
d(340000400) = 60

More numbers for you to try

Take a look at the factors page to see the factors of 340,000,400 and how to find them.

Try the factor calculator.

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