Q: What is the total or count of factors of the number 42,666,624?

 A: 384

How do I find the total factors of the number 42,666,624?

Step 1

Find the prime factorization of the number 42,666,624.

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

Factor Tree
42,666,624
Factor Arrows
221,333,312
Factor Arrows
210,666,656
Factor Arrows
25,333,328
Factor Arrows
22,666,664
Factor Arrows
21,333,332
Factor Arrows
2666,666
Factor Arrows
2333,333
Factor Arrows
3111,111
Factor Arrows
337,037
Factor Arrows
75,291
Factor Arrows
11481
Factor Arrows
1337

The prime factorization in exponential form is: 27 x 32 x 71 x 111 x 131 x 371

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.

42,666,624 = 27 x 32 x 71 x 111 x 131 x 371
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(42666624) = (7 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(42666624) = (8)(3)(2)(2)(2)(2)
Down Arrow
d(42666624) = 384

More numbers for you to try

Take a look at the factors page to see the factors of 42,666,624 and how to find them.

Try the factor calculator.

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