Q: What is the total or count of factors of the number 221,000,202?

 A: 48

How do I find the total factors of the number 221,000,202?

Step 1

Find the prime factorization of the number 221,000,202.

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

Factor Tree
221,000,202
Factor Arrows
2110,500,101
Factor Arrows
336,833,367
Factor Arrows
312,277,789
Factor Arrows
113108,653
Factor Arrows
179607

The prime factorization in exponential form is: 21 x 32 x 1131 x 1791 x 6071

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.

221,000,202 = 21 x 32 x 1131 x 1791 x 6071
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d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)
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d(221000202) = (1 + 1)(2 + 1)(1 + 1)(1 + 1)(1 + 1)
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d(221000202) = (2)(3)(2)(2)(2)
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d(221000202) = 48

More numbers for you to try

Take a look at the factors page to see the factors of 221,000,202 and how to find them.

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