Best Tutoring Websites and Coprime

The best tutoring websites make math accessible and fun. When you go to a great tutoring website, they have a way of making learning math fun again, meaning you won’t dread your next math class. A good tutor will make learning math feel more like play and less like homework. If you’re struggling with algebra or geometry or coprime, don’t hesitate to visit a tutoring website for help! These websites are designed to make it easy for students to find information quickly and get back on track. 

What is Coprime?

Coprime are numbers that have no common factors. A number is coprime to another number if when you divide both by some integer, you will get a result of 1. This can be calculated using an algorithm or a math formula. If neither number has any common factors and both these numbers are prime, then these numbers are called twin primes. 

  • Examples of coprimes include 3 and 5, 11 and 13, 29 and 31 etc. The first few examples of twin primes are: 2 & 3, 3 & 5, 5 & 7 etc. 

Coprimes are a good starting point for prime factorization, an important mathematical calculation. If two numbers are coprimes, you will get their common factors by dividing them. 

  • For example, if you divide 3 and 5, you will get 1 and 2 as their common factors. Since both these numbers have no common factors with 3 and 5 respectively, they are a coprime pair.

The sum of two coprimes is never divisible by any other number than one and itself. This is called Wilson’s theorem and states that if a+b is not divisible by any integer, then (4m)^2-1 for some m can be represented as a product of distinct primes which are none other than a and b. 

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Examples of Coprime Numbers

1, 2, 4, 6, 8, 10 are coprime. So are 1/2 and 3/4. An easy way to check if two numbers are coprime is to just add them together. If you get a non-zero answer then they’re not coprime. 

  • For example -12 is not coprime with any number because 12 + (-12) = 0. So -12 would be divisible by all positive numbers (see: prime factorization). 

The same goes for negative numbers. 

  • For example, 5 isn’t coprime with 7 because 5 + 7 = 12 which is divisible by 2 and 3. The same goes for composite numbers like 9 which isn’t coprime with 11 since 9 + 11 = 20 which is divisible by 2 and 5. The only composite number that’s coprime with itself is 1 (1 x 1 = 1). 

You can also test if a number is coprime with all other numbers (perfectly coprime) by checking whether it has any factors that aren’t even.

  •  For example, there are no odd numbers that are perfect squares – so every odd number must be coprime with all even numbers since all even numbers have factors of 2, 4, 6, and 8 which aren’t perfect squares.

Properties Related to Coprime Numbers

On Math is Fun, we have a complete list of properties for coprime numbers. Some interesting ones include: 

  1. Every natural number is coprime to 1, and every even natural number other than 2 is also coprime to 2.
  2. The product of two distinct odd primes that are not 3, 5, or 7 (such as 11 and 13) will be either a prime or a semiprime if and only if one of them has an even number of factors. 
  3. A square can always be expressed as a sum of two or more squares (i.e., if x2 = y2 then x = y ± sqrt(y2 – x2)). 
  4. Two nonzero numbers whose difference divides both into nonzero parts are called relatively prime to each other. 

To understand this specific topic and various other topics other than this, visit Cuemath to book a free session.

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