# Concept of Co-prime Number

#### definition

Co-prime numbers: Two numbers which have only 1 as a common factor are said to be co-prime or relatively prime or mutually prime numbers. For example, 10 and 21 are co-primes.

# Co-prime numbers:

### Number of Factors

1 1 1
2 1, 2 2
3 1, 3 2
4 1, 2, 4 3
5 1, 5 2
6 1, 2, 3, 6 4
7 1, 7 2
8 1, 2, 4, 8 4
9 1, 3, 9 3
10 1, 2, 5, 10 4
11 1, 11 2
12 1, 2, 3, 4, 6, 12 6
• Co-prime numbers: Two numbers which have only 1 as a common factor are said to be co-prime or relatively prime or mutually prime numbers.
• For example, 10 and 21 are co-primes, because the divisors of 10 are 1, 2, 5, 10 while the divisors of 21 are 1, 3, 7, 21 and the only factor common to both 10 and 21 is 1.
• Some other co-prime numbers are (3, 8); (4, 9); (21, 22); (22, 23); (23, 24).

#### Example

What are the common factors of 4 and 15?

These two numbers have only 1 as a common factor.

Two numbers having only 1 as a common factor are called co-prime numbers.

Thus, 4 and 15 are co-prime numbers.

#### Example

What are the common factors of 18 and 23?

These two numbers have only 1 as a common factor.

Two numbers having only 1 as a common factor are called co-prime numbers.

The numbers 1 is the factors of both 18 and 23.

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