Prime and Composite Numbers
Prime and Composite Numbers
A prime number has only two factors: 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite. The prime numbers between 2 and 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31 since each of these numbers has only two factors,1 and itself.
When the area of a rectangle is a prime number, there is only one set of possible dimensions for that rectangle. When the area of a rectangle is a composite number, there are two or more sets of possible dimensions for that rectangle. Each set of dimensions is a pair of factors.
To determine if a number is prime or composite, follow these steps:
Illustration 1: Is the number 2 prime or composite?
Solution: The factors of 2 are 1 , and 2. Hence, 2 is prime.
Illustration 2: Is the number 9 prime or composite?
Solution: The factors of 9 are 1 x 9, 3 x 3. Hence, 9 is composite.
Illustration 3: Find the composite numbers which are multiple of 5 and less than 30.
Solution: As multiples of 5 which are less than 30 are 5, 10, 15, 20, 25
Now, factors of 5 = 1,5
factors of 10 = 1, 2, 5, 10
factors of 15 = 1, 3, 5, 15
factors of 20 = 1, 2 , 4, 5 , 10, 20
factors of 25 = 1, 5, 25
As 10, 15,20, 25 has more than 2 factors, Hence all these numbers are composite.
But 5 has only two factors, so 5 is prime.
Hence, the composite numbers which are multiple of 5 and less than 30 are 10, 15, 20, 25
Which of the following numbers are co- prime? | |||
| Right Option : C | |||
| View Explanation | |||
__________ has only two factors: 1 and itself. | |||
| Right Option : A | |||
| View Explanation | |||
The smallest composite number is __________. | |||
| Right Option : C | |||
| View Explanation | |||
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