Q: What is the total or count of factors of the number 68,306,304?

 A: 128

How do I find the total factors of the number 68,306,304?

Step 1

Find the prime factorization of the number 68,306,304.

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

Factor Tree
68,306,304
Factor Arrows
234,153,152
Factor Arrows
217,076,576
Factor Arrows
28,538,288
Factor Arrows
24,269,144
Factor Arrows
22,134,572
Factor Arrows
21,067,286
Factor Arrows
2533,643
Factor Arrows
3177,881
Factor Arrows
1116,171
Factor Arrows
103157

The prime factorization in exponential form is: 27 x 31 x 111 x 1031 x 1571

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.

68,306,304 = 27 x 31 x 111 x 1031 x 1571
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(68306304) = (7 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(68306304) = (8)(2)(2)(2)(2)
Down Arrow
d(68306304) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 68,306,304 and how to find them.

Try the factor calculator.

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