Prime Numbers
Prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself
In other words, we can say prime numbers don’t have any factor other than 1 and itself.
Composite Numbers
Composite numbers are divisible by one or more numbers other than 1 and itself.
In other words, we can say that numbers having more than two factors are composite numbers.
Examples of Prime Numbers
Example 1
Is 2 is a Prime number?
Solution
Factors of 2 are
2 ÷ 1
2 is not divisible by any other number, other than 1 and itself
therefore, 2 is Prime number.
Example 2
Is 6 is a Prime number?
Solution
Factors of 6 are
6 ÷ 1 = 6
6 ÷ 2 = 3
6 ÷ 3 = 2
6 ÷ 6 = 1
6 is divisible by 1 , 2 , 3 and 6
therefore, 6 is not a Prime number.
Example 3
Is 7 is a Prime number?
Solution
Factors of 7 are 7 x 1
7 is not divisible by any other number, other than 1 and itself
therefore, 7 is Prime number.
Example 4
Is 12 is a Prime number?
Solution
Factors of 12 are
12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1
12 is divisible by 1, 2, 3, 4, 6 and 12
therefore, 12 is not a Prime number.
Examples of Composite Numbers
Example 1
Is 4 is a Composite number?
Solution
Factors of 4 are
4 ÷ 1 = 4
4 ÷ 2 = 2
Factors of 4 are 1 , 4 and 2
Therefore, 4 has more than two factors.
Hence, 4 is a Composite number.
Example 2
Is 2 is a Composite number?
Solution
Factors of 2 are
2 ÷ 1 = 2
Factors of 2 are 1 and 2
Therefore, 2 does not have more than two factors.
Hence, 2 is not a Composite number.
Example 3
Is 9 is a Composite number?
Solution
Factors of 9 are 1 x 9 , 3 x 3 and 9 x 1
Factors of 9 are 1 , 3 and 9
Therefore, 9 has more than two factors.
Hence, 9 is a Composite number.
Example 4
Is 13 is a Composite number?
Solution
Factors of 13 are 1 x 13
Factors of 13 are 1 and 13
Therefore, 13 does not have more than two factors.
Hence, 13 is not a Composite number.