Q: What is the total or count of factors of the number 263,653,000?

 A: 128

How do I find the total factors of the number 263,653,000?

Step 1

Find the prime factorization of the number 263,653,000.

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

Factor Tree
263,653,000
Factor Arrows
2131,826,500
Factor Arrows
265,913,250
Factor Arrows
232,956,625
Factor Arrows
56,591,325
Factor Arrows
51,318,265
Factor Arrows
5263,653
Factor Arrows
1320,281
Factor Arrows
171,193

The prime factorization in exponential form is: 23 x 53 x 131 x 171 x 1,1931

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)(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.

263,653,000 = 23 x 53 x 131 x 171 x 1,1931
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(263653000) = (3 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(263653000) = (4)(4)(2)(2)(2)
Down Arrow
d(263653000) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 263,653,000 and how to find them.

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