Q: What is the total or count of factors of the number 157,216,256?

 A: 80

How do I find the total factors of the number 157,216,256?

Step 1

Find the prime factorization of the number 157,216,256.

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

Factor Tree
157,216,256
Factor Arrows
278,608,128
Factor Arrows
239,304,064
Factor Arrows
219,652,032
Factor Arrows
29,826,016
Factor Arrows
24,913,008
Factor Arrows
22,456,504
Factor Arrows
21,228,252
Factor Arrows
2614,126
Factor Arrows
2307,063
Factor Arrows
378,299
Factor Arrows
43193

The prime factorization in exponential form is: 29 x 371 x 431 x 1931

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.

157,216,256 = 29 x 371 x 431 x 1931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(157216256) = (9 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(157216256) = (10)(2)(2)(2)
Down Arrow
d(157216256) = 80

More numbers for you to try

Take a look at the factors page to see the factors of 157,216,256 and how to find them.

Try the factor calculator.

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