GCD calculator
The greatest common division calculator computes GCD of two or more integers using 4 method.
Tutorial
What is Greatest common divisor (GCD)?
The greatest common divisor (factor, multiple) of two integers is the largest number that divides them both.
How to find GCF of two or more numbers?
To find the GCF of two numbers, this calculator uses the following methods:
1. Prime factorization method,
2. Repeated division method,
3. Euclidean algorithm and
4. Listing out the factors.
Examples
Method 1 : Find GCD using prime factorization method
Example: find GCD of 36 and 48
Step 1: find prime factorization of each number:
42 = 2 * 3 * 7
70 = 2 * 5 * 7
Step 2: circle out all common factors:
42 = ② * 3 * ⑦
70 = ② * 5 * ⑦
We see that the GCD is ② * ⑦ = 14
Method 2 : Find GCD using a repeated division
Example: find GCD of 84 and 140.
Step 1: Place the numbers inside division bar:
| 84 | 140 |
Step 2: Divide both numbers by 2:
| 2 | 84 | 140 |
| 42 | 70 |
Step 3: Continue to divide until the numbers do not have a common factor.
| ② | 84 | 140 |
| ② | 42 | 70 |
| ⑦ | 21 | 35 |
| 3 | 7 |
Step 4: The GCD of 84 and 140 is: ② * ② * ⑦ = 28
Method 3 : Euclidean algorithm
Example: Find GCD of 52 and 36, using Euclidean algorithm.
Solution: Divide 52 by 36 and get the remainder, then divide 36 with the remainder from previous step. When the remainder is zero the GCD is the last divisor.
| 52 | : | 36 | = | 1 | remainder (16) | ||||
| 36 | : | 16 | = | 1 | remainder (4) | ||||
| 16 | : | ④ | = | 4 | remainder (0) | ||||
We conclude that the GCD = 4.
Method 4 : Listing out the factors
Example: find GCD of 45 and 54 by listing out the factors.
Step 1: Find divisors for the given numbers:
The divisors of 45 are 1, 3, 5, ⑨, 15 and 45
The divisors of 54 are 1, 2, 3, 6, ⑨ 18, 27 and 54
Step 2: The greatest divisor = ⑨
Find Greatest Common Divisor of 10 and 15, using prime factorization.
solution
The GCD of given numbers is 5.
explanation
Step 1 : Find prime factorization of each number.
$$\begin{aligned}10 =& 2\cdot5\\[8pt]15 =& 3\cdot5\\[8pt]\end{aligned}$$(view steps on how to factor 10 and 15. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}10 =& 2\cdot\color{blue}{\boxed{5}}\\[8pt]15 =& 3\cdot\color{blue}{\boxed{5}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 5 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.
1. GCD Definition, Methods, Examples
2. Euclidean Algorithm - video tutorial
3. Program to Find GCD - code implementation in C++, C, Java, Python, C# and Javascript.