# Here’s a lesson on Prime vs. Composite Numbers

Subject:

Math

9, 10, 11, 12

Title – How to determine whether a number is prime or composite
By – Anne Canito
Subject – Math
Grade Level – 9 – 12
A prime number is an integer greater than 1 which has no factors besides 1 and itself. (For example 5 is divisible evenly by only 1 and 5, therefore it is prime).

Remember-

– The number 1 is NOT a prime because the definition states that the integer has to be greater than 1

– Two is the only even prime number, since every even number thereafter is divisible by 2

A composite number is a nonprime integer. (For example, 9 is a composite number because it is divisible evenly by 1, 3, and 9)

Rules of testing whether a number is prime or composite:

– If a number is even, unless it is 2 it is always composite

-If a number’s digits add up to a number which is divisible by 3, it is divisible by 3 and therefore composite.
(246- 2+4+6=12 12/3=4 therefore it is composite)

Rather large numbers-

for example sake I’ll use the number 2,321

1) Find the square root of the number (The Square root of 144 is 12 because 12*12=144)
– The Square root of 2,321 is 48.176…

2) remember that if the square root results in an integer it is automatically composite

3) if your number ends in a 0,2,4,5,6,8 it is NOT PRIME
– 2,321 ends in a 1, so we keep going

4) add up the digits of your number, if the sum is divisible by 3, your number is composite
-2+3+2+1= 8 3 does not go into 8 evenly- onto the next
step

5) Divide the number by all the prime numbers less than the square root (you can skip 2, 3, and 5)
-since the square root of 2,321 is 48.176…, we need to
try dividing 2,321 by primes less than 48
(7,11,13,17,19,23,29,31,37,41,43,47) since 2,321 is
divisible by 11, it is NOT prime and therefore composite.

6) If a number is not divisible by any of the prime numbers less than the square, it is PRIME, if it is, it’s COMPOSITE

TEST THE SKILLS YOU HAVE LEARNED-

Directions state whether the number is prime, composite, or neither:

1) 27

2) 22.31

3) 4/3

4) 242

5) 1

6) 192

7) 169

8) 0

9) 3,475

10) 211

11) 91

12) 87

13) 227

14) 119

15) 143

BONUS:

There is a set of 13 consecutive composite numbers in the integers 1-200. What is the smallest integer of this set?