Q: What is the total or count of factors of the number 53,122,025?

 A: 36

How do I find the total factors of the number 53,122,025?

Step 1

Find the prime factorization of the number 53,122,025.

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

Factor Tree
53,122,025
Factor Arrows
510,624,405
Factor Arrows
52,124,881
Factor Arrows
11193,171
Factor Arrows
1117,561
Factor Arrows
171,033

The prime factorization in exponential form is: 52 x 112 x 171 x 1,0331

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.

53,122,025 = 52 x 112 x 171 x 1,0331
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(53122025) = (2 + 1)(2 + 1)(1 + 1)(1 + 1)
Down Arrow
d(53122025) = (3)(3)(2)(2)
Down Arrow
d(53122025) = 36

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Take a look at the factors page to see the factors of 53,122,025 and how to find them.

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