Question

How to find coprime numbers and prime numbers and
Prime triplet numbers

Answer 1

Answer:

PRIME NUMBER

A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1.

To find whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number

CO-PRIME NUMBER

Co-prime number is a set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF) will be 1

It is important that there should be two numbers in order to form co-primes.

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.

Example 1: 21 and 22

For 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.

PRIME TRIPLETS

A prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form (p, p + 2, p + 6) or (p, p + 4, p + 6). With the exceptions of (2, 3, 5) and (3, 5, 7), this is the closest possible grouping of three prime numbers, since one of every three sequential odd numbers is a multiple of three, and hence not prime (except for 3 itself).

Step-by-step explanation: