Greatest Common Factor of 18 and 36

How to find the Greatest Common Factor of 18 and 36?

There are many methods we can apply to calculate the GCF of 18 and 36.

In our first method, we'll find out the prime factorisation of the 18 and 36 numbers.

In our second method, we'll create a list of all the factors of the 18 and 36 numbers.

These are the numbers that divide the 18 and 36 numbers without a remainder.

Once we have these, all we have to do is to find the one that is the biggest common number from the 2 lists.

Now let's look at each methods, and calculate the GCF of 18 and 36.

Methods of calculating the GCF of 18 and 36:

Prime Factorisation
List of factors
Euclidean algorithm
Binary Greatest Common Divisor algorithm

Method 1 - Prime Factorisation

With the prime factorisation method, all we have to do is to find the common prime factors of 18 and 36, and then multiply them. Really simple:

Step 1: Let's create a list of all the prime factors of 18 and 36:

Prime factors of 18:

As you can see below, the prime factors of 18 are 2, 3 and 3.

Let's illustrate the prime factorization of 18 in exponential form:

18 = 2¹x3²

Prime factors of 36:

As you can see below, the prime factors of 36 are 2, 2, 3 and 3.

Let's illustrate the prime factorization of 36 in exponential form:

36 = 2²x3²

Step 2: Write down a list of all the common prime factors of 18 and 36:

As seen in the boxes above, the common prime factors of 18 and 36 are 2, 3 and 3.

Step 3: All we have to do now is to multiply these common prime factors:

Find the product of all common prime factors by multiplying them:

2¹x3²=18

Done!

According to our calculations above, the Greatest Common Factor of 18 and 36 is 18

Method 2 - List of Factors

With this simple method, we'll need to find all the factors of 18 and 36, factors are numbers that divide the another number without a remainder, and simply identify the common ones, then choose which is the largest one.

Step 1: Create a list of all the numbers that divide 18 and 36 without a remainder:

List of factors that divide 18 without a remainder are:

1, 2, 3, 6, 9 and 18.

List of factors that divide 36 without a remainder are:

1, 2, 3, 4, 9, 12, 18 and 36.

Step 2: Identify the largest common number from the 2 lists above:

As you can see in the lists of factors from above, for the numbers 18 and 36, we have highlighted the number 18, which means that we have found the Greatest Common Factor, or GCF.

According to our calculations above, the Greatest Common Factor of 18 and 36 is 18

Method 3 - Euclidean algorithm

The Euclidean algorithm says that if number k is the GCM of 18 and 36, then the number k is also the GCM of the division remainder of the numbers 18 and 36.

We follow this procedure until the reminder is 0.

The Greatest Common Divisor is the last nonzero number.

Step 1: Sort the numbers into ascending order:

18, 36

Step 2

Take out, from the set, the smallers number as you divisor: 18

The remaining set is: 36

Find the reminder of the division between the number and the divisor

36 mod 18 = 0

Gather the divisor and all of the remainders and sort them in ascending order. Remove any duplicates and 0. Our set is:

Step 3: Take the remaining number from our set

The Greatest Common Factor of 18 and 36 is 18

Method 4 - Binary Greatest Common Divisor algorithm

The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction.

Although the algorithm in its contemporary form was first published by the Israeli physicist and programmer Josef Stein in 1967, it may have been known by the 2nd century BCE, in ancient China.