Q: What is the total or count of factors of the number 153,543,360?

 A: 224

How do I find the total factors of the number 153,543,360?

Step 1

Find the prime factorization of the number 153,543,360.

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

Factor Tree
153,543,360
Factor Arrows
276,771,680
Factor Arrows
238,385,840
Factor Arrows
219,192,920
Factor Arrows
29,596,460
Factor Arrows
24,798,230
Factor Arrows
22,399,115
Factor Arrows
3799,705
Factor Arrows
5159,941
Factor Arrows
413,901
Factor Arrows
4783

The prime factorization in exponential form is: 26 x 31 x 51 x 411 x 471 x 831

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.

153,543,360 = 26 x 31 x 51 x 411 x 471 x 831
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(153543360) = (6 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(153543360) = (7)(2)(2)(2)(2)(2)
Down Arrow
d(153543360) = 224

More numbers for you to try

Take a look at the factors page to see the factors of 153,543,360 and how to find them.

Try the factor calculator.

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