Q: What is the prime factorization of the number 132,661,187?

 A:
  • The prime factors are: 11,093 x 11,959
    • or also written as { 11,093, 11,959 }
  • Written in exponential form: 11,0931 x 11,9591

Why is the prime factorization of 132,661,187 written as 11,0931 x 11,9591?

What is prime factorization?

Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.

Finding the prime factors of 132,661,187

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

If it doesn't make sense yet, let's try it...

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 132,661,187 by 2

132,661,187 ÷ 2 = 66,330,593.5 - This has a remainder. Let's try another prime number.
132,661,187 ÷ 3 = 44,220,395.6667 - This has a remainder. Let's try another prime number.
132,661,187 ÷ 5 = 26,532,237.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
132,661,187 ÷ 11,093 = 11,959 - No remainder! 11,093 is one of the factors!
11,959 ÷ 11,093 = 1.0781 - There is a remainder. We can't divide by 11093 evenly anymore. Let's try the next prime number
11,959 ÷ 11,113 = 1.0761 - This has a remainder. 11,113 is not a factor.
11,959 ÷ 11,117 = 1.0757 - This has a remainder. 11,117 is not a factor.
11,959 ÷ 11,119 = 1.0755 - This has a remainder. 11,119 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
11,959 ÷ 11,959 = 1 - No remainder! 11,959 is one of the factors!

The orange divisor(s) above are the prime factors of the number 132,661,187. If we put all of it together we have the factors 11,093 x 11,959 = 132,661,187. It can also be written in exponential form as 11,0931 x 11,9591.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 132,661,187.

132,661,187
Factor Arrows
11,09311,959

More Prime Factorization Examples

132,661,185132,661,186132,661,188132,661,189
31 x 51 x 1,6131 x 5,483121 x 71 x 2111 x 44,909122 x 32 x 111 x 5211 x 6431132,661,1891

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