Q: What is the total or count of factors of the number 265,398?

 A: 32

How do I find the total factors of the number 265,398?

Step 1

Find the prime factorization of the number 265,398.

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

Factor Tree
265,398
Factor Arrows
2132,699
Factor Arrows
344,233
Factor Arrows
76,319
Factor Arrows
7189

The prime factorization in exponential form is: 21 x 31 x 71 x 711 x 891

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.

265,398 = 21 x 31 x 71 x 711 x 891
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
Down Arrow
d(265398) = (1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(265398) = (2)(2)(2)(2)(2)
Down Arrow
d(265398) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 265,398 and how to find them.

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