Q: What is the prime factorization of the number 315,487?

 A:
  • The prime factors are: 31 x 10,177
    • or also written as { 31, 10,177 }
  • Written in exponential form: 311 x 10,1771

Why is the prime factorization of 315,487 written as 311 x 10,1771?

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 315,487

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 315,487 by 2

315,487 ÷ 2 = 157,743.5 - This has a remainder. Let's try another prime number.
315,487 ÷ 3 = 105,162.3333 - This has a remainder. Let's try another prime number.
315,487 ÷ 5 = 63,097.4 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
315,487 ÷ 31 = 10,177 - No remainder! 31 is one of the factors!
10,177 ÷ 31 = 328.2903 - There is a remainder. We can't divide by 31 evenly anymore. Let's try the next prime number
10,177 ÷ 37 = 275.0541 - This has a remainder. 37 is not a factor.
10,177 ÷ 41 = 248.2195 - This has a remainder. 41 is not a factor.
10,177 ÷ 43 = 236.6744 - This has a remainder. 43 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
10,177 ÷ 10,177 = 1 - No remainder! 10,177 is one of the factors!

The orange divisor(s) above are the prime factors of the number 315,487. If we put all of it together we have the factors 31 x 10,177 = 315,487. It can also be written in exponential form as 311 x 10,1771.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 315,487.

315,487
Factor Arrows
3110,177

More Prime Factorization Examples

315,485315,486315,487315,488315,489315,490315,491
51 x 63,097121 x 32 x 171 x 1,0311311 x 10,177125 x 9,859131 x 1031 x 1,021121 x 51 x 71 x 4,5071111 x 231 x 291 x 431
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