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## What is Co Prime Number

Pairs of numbers whose factors do not have any common factor other than 1 are called co-prime numbers.

In other words – a set of at least 2 prime numbers whose HCF is 1 is called co-prime numbers.

HCF stands for Greatest Common Factor. Like :- The biggest common factor in 9, 25 is only 1. Hence (9, 25) is a co-prime number.

**Example :-** (5, 7), (2, 3)

Co-prime number is called Co-Prime Number in English.

**Note :-**

- Co-prime numbers always occur in pairs.
- Any two consecutive numbers are co-prime numbers. For example:- (1, 2), (2, 3), (3, 4)……etc.
- 0 forms the only co-prime number with 1 and -1. For example:- (0, 1), (0, -1)
- It is not necessary that both the numbers should be prime in co-prime numbers.
- 2 Composite numbers can also be co-prime numbers.
- For example:- 8 and 15 here both the numbers are divisible.
- Only 1 comes in the common factor in 8 and 15, so both these numbers are also co-prime numbers.
- In co-prime numbers, it is not necessary that both the numbers or one number should be prime.

## Problems Based on Co Prime Numbers

Question 1. Which of the given factors (2, 3), (3, 4), (5, 6), (14, 15), ……………. are co-prime numbers?

Solution :- (2, 3), (3, 4), (5, 6), (14, 15),

We can also understand co-prime numbers in this way –

**As :-**

(2, 3)

2 × 1 = 2

3 × 1 = 3

(3, 4)

3 × 1 = 3

4 × 1 = 4

(5, 6)

5 × 1 = 5

6 × 1 = 6

(14, 15)

14 × 1 = 14

15 × 1 = 15

In factorization, you can see that all of them have a common 1, that is, they are co-prime numbers.

Question 2. Are the given factors co-prime (14, 15)?

Solution :- In factorization (14, 15),

Divisors of 14 :- 1, 2, 7, 14

Divisors of 15 :- 1, 3, 5, 15

The factors of 14 and 15 have no common number other than 1. So 14 and 15 have only one common factor. Hence 14 and 15 are co-prime numbers.

Question 3. Write the pairs of prime numbers less than 10 whose difference is 2.

Solution :- According to the question,

Prime numbers less than 10 – 2, 3, 5, 7

Numbers with difference of 2 between prime numbers less than 10 = (3, 5), (5, 7)

Answer: (3, 5), (5, 7)

Question 4. Write the pairs of prime numbers less than 20 whose difference is 2.

Solution :- According to the question,

Prime numbers less than 20 – 2, 3, 5, 7, 11, 13, 17, 19

Difference of 2 between prime numbers less than 20 = (3, 5), (5, 7), (11, 13), (17, 19)

Answer: (3, 5), (5, 7), (11, 13), (17, 19)

Question5. Write such pairs of prime numbers less than 50 whose difference is 1.

Solution :- According to the question,

prime numbers less than 50

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Difference of 1 between prime numbers less than 50 (3 – 2 ) = 1

Answer: (2, 3)

### FAQ

**Q.1 What is co-prime numbers with examples?**

**Ans. **Co-prime Numbers. Co-prime numbers are pairs of numbers that do not have any common factor other than 1.

**Q.2 Is 5 and 7 co-prime?**

**Ans. **Co prime numbers between 1 and 50 are (2, 3), (3, 5), (5, 7), (11, 13), (17, 19), (21, 22), (29, 31) and (41, 43).

**Q.3 What are the co-prime numbers from 1 to 100?**

**Ans.** (2,3), (3,5), (5,7), (11,13), (17,19), (21,22), (29,31), (41,43), (59,61), (71,73), (87,88), (99,100), (28,57), (13,14), these are some of coprime numbers from 1 to 100. When we consider any pair of the above, when we determine the greatest common factor will be 1.

**Q.4 Is 27 and 72 a co-prime?**

**Answer.** 27 and 72 are not Co-Prime (relatively, mutually prime) – if they have common prime factors, that is, if their greatest (highest) common factor (divisor), gcf, hcf, gcd, is not 1.

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Whole Number | Integer Number | Prime Numbers |

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