Handy Tool i.e., GCD Calculator makes your calculations so fast and simple. All you have to provide is a given number in the input field of the calculator and click on the calculate button. That's it, you will get the greatest common divisor of given numbers in a fraction of seconds.
Ex: GCD of 24, 48, 64 (or) GCD of 16, 56, 12 (or) GCD of 8, 72, 48
Here are some samples of GCD of Numbers calculations.
GCD Calculator: Are you searching for the simplest way to find out the GCD of given numbers along with a complete guide about the Greatest common divisor? Then, you have come to the correct page. Here, students can find almost every detail about the Greatest common divisor of given numbers concept with detailed explanation. Apart from this, you can also get knowledge about the methods that we need to use for calculating the GCD like factoring, prime decomposition, GCD formula with the procedure, and solved examples. So, make use of this GCD Calculator and determine the largest divisor that divides the number evenly within no time.
In Maths, the Greatest Common Divisor (GCD) is defined as the largest positive integer that divides each of the integers evenly with the remainder zero. The greatest common divisor is also called the Greatest common denominator(GCD) or Highest Common Factor (HCF). We can denote the greatest common divisor of two integers a and b as GCD(a,b).
How to Find the Greatest Common Divisor or Denominator(GCD)?
Calculating the GCD of numbers can be tricky manually. But there are various techniques that determine the Greatest Common Divisor of given numbers easily by hand. Here, we have taken the most commonly used & standard methods to solve the GCD of numbers, and also you can learn the concept by the provided detailed procedure & show work.
You can select any of the methods that fit to solve the given numbers and find out the Greatest common divisor quickly & easily. Take a look at the methods that you can use to solve GCD here with a detailed explanation & solved examples.
Procedure to Solve GCD of Numbers using the List of Factors method
Find the GCD of 48, 36, and 124 using a list of factors method?
Given numbers are 48, 36, 124
The common divisor from each set of factors is 1, 2, 4 and we see that the largest divisor is 4.
Thus, the Greatest Common Divisor of 48, 36, 124 is 4.
Steps to Solve Greatest Common Denominator or Divisor using Prime Factorization
Greatest common divisors can be calculated by determining the prime factorizations of the given numbers. Yes, prime factor decomposition is the most commonly used method to compute the GCD of given numbers. The steps comprised in computing the Greatest common divisor using prime factorization are as follows:
Solve the GCD of 16, 88, 104 by prime decomposition?
Given numbers are 16, 88, 104
Prime factors of 16 = 2 × 2 × 2 × 2
Prime factors of 88 = 2 × 2 × 2 × 11
Prime factors of 104 = 2 × 2 × 2 × 13
Now product the common prime factor and get the greatest common divisor
Thus, GCF(16, 88, 104) = 2 × 2 × 2 = 8.
How to Calculate GCD of two numbers by GCD Formula?
One more prominent method to calculate the GCD is by using the GCD formula. If a and b are both nonzero, the greatest common divisor of a and b can be calculated with the help of the least common multiple (lcm) of a and b:
GCD(a,b) = a×b / LCM(a,b)
Steps to solve Greatest Common Divisor Using GCD formula:
Find GCD of 23 and 45 using formula?
Given numbers are 23 and 45
The formula to find the greatest common divisor of two numbers is
GCD(a, b) = a x b / LCM(a, b)
GCD(23, 45) = 23*45 / LCM(23, 45)
GCD(23, 45) = 1035 / LCM(23, 45)
we get LCM of 23 and 45 is 1035 by applying primes
Now apply LCM(23, 45) in the formula and we get GCD of 23 and 45
GCD(23, 45) = 1035 / 1035
GCD(23, 45) = 1
Therefore, the greatest common divisor or greatest common denominator of 23 and 45 is 1.
See help from lcmgcf.com to know all about the GCF, LCD, LCM, HCF Concepts, and understand them easily.
1. What is the full form of GCD?
The Full Form of GCD is Greatest Common Divisor.
2. What is the GCD of two numbers?
GCD of two numbers is the largest number that divides them both equally with the remainder zero. Also, the GCD of two numbers known as the Greatest Common Factor or Highest Common Factor of two numbers.
3. How do you find the GCD of Given Numbers?
Finding the GCD of two or more given numbers can be simple by following the detailed steps provided over here using various standard methods. Check out the GCD of numbers using prime factorization, or other methods explanation from our page & find out GCD easily. Also, you can use handy tools provided by lcmgcf.com for quick results.
4. Is GCD and HCF the same?
Yes, GCD and HCF are the same. GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of numbers is the greatest number or divisor or factor that divides the given numbers evenly with the remainder zero. For instance, GCD of 20 and 28 is 4 then HCF of 20 and 28 is also 4.