Q: What is the total or count of factors of the number 103,350,546?

 A: 128

How do I find the total factors of the number 103,350,546?

Step 1

Find the prime factorization of the number 103,350,546.

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

Factor Tree
103,350,546
Factor Arrows
251,675,273
Factor Arrows
317,225,091
Factor Arrows
35,741,697
Factor Arrows
31,913,899
Factor Arrows
13147,223
Factor Arrows
236,401
Factor Arrows
37173

The prime factorization in exponential form is: 21 x 33 x 131 x 231 x 371 x 1731

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.

103,350,546 = 21 x 33 x 131 x 231 x 371 x 1731
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)
Down Arrow
d(103350546) = (1 + 1)(3 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(103350546) = (2)(4)(2)(2)(2)(2)
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d(103350546) = 128

More numbers for you to try

Take a look at the factors page to see the factors of 103,350,546 and how to find them.

Try the factor calculator.

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