Q: What is the total or count of factors of the number 5,186,544?

 A: 120

How do I find the total factors of the number 5,186,544?

Step 1

Find the prime factorization of the number 5,186,544.

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

Factor Tree
5,186,544
Factor Arrows
22,593,272
Factor Arrows
21,296,636
Factor Arrows
2648,318
Factor Arrows
2324,159
Factor Arrows
3108,053
Factor Arrows
119,823
Factor Arrows
11893
Factor Arrows
1947

The prime factorization in exponential form is: 24 x 31 x 112 x 191 x 471

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.

5,186,544 = 24 x 31 x 112 x 191 x 471
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(5186544) = (4 + 1)(1 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(5186544) = (5)(2)(3)(2)(2)
Down Arrow
d(5186544) = 120

More numbers for you to try

Take a look at the factors page to see the factors of 5,186,544 and how to find them.

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