Question

Write some example if p and q has no common factor other than.write the property of q.

Answer 1

Co-prime number is a set of numbers or integers which have only 1 as their common factor. That is their highest common factor (HCF) will be 1. It is also known as relatively prime or mutually prime numbers.

Consider a set of two numbers, if they have no positive integer that can divide both other than 1, the pair of numbers is co-prime.

Ex 1: 21 and 22

21 and 22:

• The factors of 21 are 1, 3, 7 and 21.
• The factors of 22 are 1, 2, 11 and 22.

Here 21 and 22 have only one common factor that is 1.Hence their HCF is 1 and are co-prime.

Ex 2: 21 and 27

21 and 27:

• The factors of 21 are 1, 3, 7 and 21.
• The factors of 27 are 1, 2, 3, 9 and 27.

Here 21 and 27 have two common factors they are 1 and 3. HCF is 3 and they are not co-prime.

PROPERTIES OF CO-PRIME NUMBERS

Some of the properties of co-prime numbers are as follows.

1. 1 is co-prime with every number.
2. Every prime number is co-prime to each other: As every prime number have only two factors 1 and the number itself, the only common factor of two prime numbers will be 1.For example, 2 and 3 are two prime numbers. Factors of 2 are 1, 2 and factors of 3 are 1, 3. The only common factor is 1 and hence is co-prime.
3. Any two successive numbers/ integers are always co-prime: Take any consecutive number such as 2, 3 or 3, 4 or 5, 6 and so on; they have 1 as their HCF.
4. The sum of any two co-prime numbers are always co-prime with their product: 2 and 3 are co-prime and have 5 as their sum (2+3) and 6 as the product (2×3). Hence, 5 and 6 are co-prime to each other.