04 Mar 2024

What is a co-prime number?

We all are aware of what a prime number is. So, what is a co-prime number? Math can be fascinating because we discover many interesting facts through it. Read on for more.

Co-prime numbers have no mutual factor other than 1. A set of co-prime numbers must contain at least two figures. For example, 4 and 7 have only 1 as their maximum common feature. Co-prime numbers are also shaped by two composite numbers, 4 and 9.

What is a co-prime numbers?

Co-prime Numbers are a collection of integers or numbers that stake only the number 1 as a shared factor.
For instance, x and y are two positive numbers co-prime if and only if they have one common aspect, and thus HCF(x, y) = 1. In other words, co-prime numbers are a duo of numbers or integers with only one mutual factor, namely that their uppermost mutual factor (HCF) is 1. Co-prime numbers are also known as equally prime numbers or relatively prime numbers. It is serious to have two numbers to procedure co-primes.

How do I find co-prime numbers?

Think of a duo of numbers; if no positive integer other than one can divide them, the two are co-prime.

Illustration 1- 21 and 22

For figures 21 and 22-

 Figure Features 21 1, 3, 7 22 1, 2, 11

Now, 21 and 22 shares only one factor, that is 1. As an outcome, the HCF is 1, and they are co-prime.

Illustration 2- 21 and 27

For Figures 21 and 27-

 Figure Features 21 1, 3, 7 27 1, 3, 9

In this case, 21 and 27 dividends two features, 1 and 3. They had an HCF of 3 and are no co-prime.

Co-prime figures list

Pair of Co-prime number duos

1                (1,7), 8(1,8),  22(1, 22)
2 3(2,3), 5(2,5), 7(2,7), 9(2, 9), 11(2, 11), 13(2,13), 15(2,15)
3 4(3,4), 5(3,5), 7(3,7), 10(3, 10), 11(3, 11), 15(3, 15), 22(3, 22)
4 5(4,5), 7(4,7), 9(4,9), 11(4, 11), 13(4, 13), (154, 15), 17(4, 17)
5 6(5,6), 7(5 7), 8(5,8), 9(5,9), 11(5, 11), 12(5, 12), 14(5, 14)

Properties

Co-prime numbers have six properties.

The universal co-prime number is One. You can combine one with any numeral, and they will be co-prime. For instance, (1,2), (1,3), (1,8), (1,15), (1,532), (1,2568).

In a number order, the integer instantly following and preceding a number is co-prime. For example, the number 33; thus, the number following 33 will be 34, which is co-prime to 33. Therefore, the number before 33 is 32; 33 is a co-prime.

Because 0 is a factor-less number, it is not co-prime with any other numeral.

Even numbers can not ever be co-prime because they all are part of a common factor other than 1, which is 2.

If we multiply two co-prime numbers, the resulting numbers are also co-prime. For illustration, 3+4 = 7, and 3 x 4 = 12, the outcomes 7 and 12 have only one mutual factor; thus, they are co-prime.

An odd number and an even number are also co-prime. However, if the figures have 0 and 5 at the ones or unit places, they are not co-prime because they have an HCF = 5.

Prime numbers are co-prime numbers. For sample,  (11,13); 11=1×11 & 13= 1×13

Co-prime and twin prime numbers

The set of two numbers with precisely one composite number is known as twin prime numbers.

Co-prime numbers have an HCF of one. Matching prime numbers, on the other hand, are prime numbers with a change of two. For example, 7 and 5 are twin prime numbers. The following points distinguish co-prime and twin-prime numbers.

Twin prime number

The difference between two primes will be any whole number. The difference between two twin primes is always two.
Co-prime numbers can be either prime numbers or composite numbers. Twin prime numbers are always prime numbers.
Co-prime numbers can be twin prime numbers or not. All twin prime number sets are co-prime.
Any number can join 1 to form a co-prime pair. 1 form a twin prime duo only with 3. For cases 1 and 3 as (3-1=2)

Co-prime numbers from 1 to 100

There are several pairs of primes reaching from 1 to 100. Among them are-

• 13 and 14
• 28 and 57
• 1 and 99
• 2 and 97
• 46 and 67
• (75 and 41)

Therefore, any number with a mixture of 1 can be written as a co-prime pair, Like  (22,1), (31,1), (4,1), (90,1), (1,100). Numerous co-prime numbers from 1 to 100 are defined in this manner.

Key takeaways

The co-prime numbers do not have to be a prime number. It is also known as a composite number.

Any two prime numbers given must be a Co-prime.

Sets of two even numbers can never be co-prime.

Any number can form a co-prime pair with 1 (one).

Any two consecutive numbers are indeed co-prime.

Two even numbers can never be co-prime.

Co-prime numbers need not be prime numbers. For instance, 12 and 35 are co-prime numbers. Therefore, 12 and 35 are not prime numbers.

FAQs

Q1. What is the coprime of 60?

Answer- For instance, 60 is divided by two to profit 30, divided by two to yield 15, and divided by three to profit five (another prime). Hence, 60 = 2 × 2 × 3 × 5.

Q2. What is the smallest co-prime number?

Answer- 2 is the smallest prime number. A number must have only two aspects- 1 and the number itself to be prime.

Q3. How do you check if two numbers are co-prime?

Answer- If the greatest common divisor of two numbers, X and Y, is 1, they are said to be Co-prime or mutually prime.