Q: What is the total or count of factors of the number 378,488?

 A: 48

How do I find the total factors of the number 378,488?

Step 1

Find the prime factorization of the number 378,488.

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

Factor Tree
378,488
Factor Arrows
2189,244
Factor Arrows
294,622
Factor Arrows
247,311
Factor Arrows
114,301
Factor Arrows
11391
Factor Arrows
1723

The prime factorization in exponential form is: 23 x 112 x 171 x 231

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.

378,488 = 23 x 112 x 171 x 231
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(378488) = (3 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(378488) = (4)(3)(2)(2)
Down Arrow
d(378488) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 378,488 and how to find them.

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