Factorization

When a number is decomposed into two smaller numbers such that the product of two smaller numbers equals the original number, then the process is called Factorization. The two smaller numbers are factors.

e.g.

8 => 2, 4 because 8 = 2 x 4

15 => 3, 5 because 15 = 3 x 5

We can continue the process as a factor itself may also be decomposed into another two smaller numbers.

Prime number

2, 3, 5, 7, 11… are prime numbers. We cannot find any two smaller numbers such that the product equals this number.

 

Relationship between Prime number and Factor

A non-prime number can be decomposed into two smaller numbers or factors. A factor can be further decomposed if it is non-prime. The process can be continued until all the smaller factors are prime numbers.

e.g.

8 (=2 x 4) => 2, 4 => 2, 2, 2

30 (= 6 x 5) => 6, 5 => 2, 3, 5

Another interesting thing is that when a prime number (other than 2) +1 or -1, it will become a non-prime number. Since it is non-prime, it can be decomposed into factors. These factors can be further decomposed if non-prime. If they are prime numbers, use the magic of +1 or -1 to turn it into a non-prime number and continue the process.

e.g. 37 is a prime number

37 – 1 = 36 (36 => 2, 3, 6)

37 + 1 = 38 => 2, 19 (19 -1 = 18 => 3, 6)

You can see that

37 = 2 x 3 x 6 + 1

37 = (3 x 6 + 1) x 2 – 1

37 = (2 x 5 – 1) x 4 + 1

 

Question: when you have only eight numbers: 2, 3, 4, 5, 6, 7 (for multiplication only) +1 and -1, can you form the number of 77 or 99?

Check out the “SmartBoard – Math” in App Store if you are up for the challenge!

 

Prime number and Factorization

2 thoughts on “Prime number and Factorization

Leave a Reply

Your email address will not be published. Required fields are marked *