Q: What is the total or count of factors of the number 433,414,100?

 A: 72

How do I find the total factors of the number 433,414,100?

Step 1

Find the prime factorization of the number 433,414,100.

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

Factor Tree
433,414,100
Factor Arrows
2216,707,050
Factor Arrows
2108,353,525
Factor Arrows
521,670,705
Factor Arrows
54,334,141
Factor Arrows
7619,163
Factor Arrows
3119,973

The prime factorization in exponential form is: 22 x 52 x 71 x 311 x 19,9731

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)(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.

433,414,100 = 22 x 52 x 71 x 311 x 19,9731
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(433414100) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(433414100) = (3)(3)(2)(2)(2)
Down Arrow
d(433414100) = 72

More numbers for you to try

Take a look at the factors page to see the factors of 433,414,100 and how to find them.

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