Properties of Co-Prime Numbers
Some of the properties of co-prime numbers are as follows.
1 is co-prime with every number.
Any two prime numbers are co-prime to each other: As every prime number has 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 they are co-prime.
Any two successive numbers/ integers are always co-prime: Take any consecutive numbers such as 2, 3, or 3, 4 or 5, 6, and so on; they have 1 as their HCF.
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.
Two even numbers can never form a coprime pair as all the even numbers have a common factor as 2.
If two numbers have their unit digits as 0 and 5, then they are not coprime to each other. For example 10 and 15 are not coprime since their HCF is 5 (or divisible by 5).
Co prime numbers from 1 to 100
There are several pairs of co-primes from 1 to 100 which follow the above properties. Some of them are:
(13, 14)
(28, 57)
(1, 99)
(2, 97)
(46, 67)
(75, 41) and so on.
Also, we can write any number with the combination of 1 as a coprime pair such as (22, 1), (31, 1), (4, 1), (90, 1), (1, 100). In this way, many coprime numbers are defined from 1 to 100.
Answers
Answer:
Properties of Co-Prime Numbers
Some of the properties of co-prime numbers are as follows.
1 is co-prime with every number.
Any two prime numbers are co-prime to each other: As every prime number has 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 they are co-prime.
Any two successive numbers/ integers are always co-prime: Take any consecutive numbers such as 2, 3, or 3, 4 or 5, 6, and so on; they have 1 as their HCF.
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.
Two even numbers can never form a coprime pair as all the even numbers have a common factor as 2.
If two numbers have their unit digits as 0 and 5, then they are not coprime to each other. For example 10 and 15 are not coprime since their HCF is 5 (or divisible by 5).
Co prime numbers from 1 to 100
There are several pairs of co-primes from 1 to 100 which follow the above properties. Some of them are:
(13, 14)
(28, 57)
(1, 99)
(2, 97)
(46, 67)
(75, 41) and so on.
Also, we can write any number with the combination of 1 as a coprime pair such as (22, 1), (31, 1), (4, 1), (90, 1), (1, 100). In this way, many coprime numbers are defined from 1 to 100..