Q: What is the prime factorization of the number 987,543,247?

 A:
  • The prime factors are: 987,543,247
    • or also written as { 987,543,247 }
  • Written in exponential form: 987,543,2471

Why is the prime factorization of 987,543,247 written as 987,543,2471?

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 987,543,247

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 987,543,247 by 2

987,543,247 ÷ 2 = 493,771,623.5 - This has a remainder. Let's try another prime number.
987,543,247 ÷ 3 = 329,181,082.3333 - This has a remainder. Let's try another prime number.
987,543,247 ÷ 5 = 197,508,649.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
987,543,247 ÷ 987,543,247 = 1 - No remainder! 987,543,247 is one of the factors!

The orange divisor(s) above are the prime factors of the number 987,543,247. If we put all of it together we have the factors 987,543,247 = 987,543,247. It can also be written in exponential form as 987,543,2471.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 987,543,247.

More Prime Factorization Examples

987,543,245987,543,246987,543,248987,543,249
51 x 131 x 3791 x 40,087121 x 31 x 371 x 431 x 103,451124 x 61,721,453131 x 71 x 111 x 231 x 185,8731
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