GCF of 36 and 48

The greatest common factor of the two numbers is the largest number by which the numbers 36 and 48 can be completely divided. In order to find the GCF of two or more numbers, we will find their factors and the largest factor among the listed factors.

For example, the GCF of 36 and 48 is 12. This means that 12 is the largest number that can evenly divide both 36 and 48.
 

We have learned that listing the prime factors of the numbers is one of the methods to determine the largest common factor. Next, we will also discuss other methods to find the GCF.

The methods to find the GCF of 36 and 48 are mentioned below:

• Listing Factors Method
• Prime Factorization Method
• Euclidean Algorithm Method
   

The easiest method to determine the GCF is through the listing factors method, where the factors divide the input numbers evenly. We will now find the GCF by following the step-by-step method given below:

Step 1: Find out the factors of 36 and 48

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

Step 2: Pick out the numbers that divide both 36 and 48 evenly from the numbers listed above. Hence, the common factors of 36 and 48 are 1, 2, 3, 4, 6 and 12

Step 3: The largest common factor will be the GCF of 36 and 48.
Therefore, the GCF of 36 and 48 is 12
 

In the prime factorization method, we first express the numbers 36 and 48 in terms of their prime factors. From the prime factors of 36 and 48, we find the common prime factors with the smallest powers and take their product to find the GCF of 36 and 48.

To find the GCF of 36 and 48, follow the steps given below:

Step 1: Prime factorize the given numbers 36 and 48

Step 2: Prime factorization of 36 = 22 × 32 = 2 × 2 × 3 × 3
Prime factorization of 48 = 2⁴ × 3¹ = 2 × 2 × 2 × 2 × 3

Step 3: Now, find the prime factors with the smallest powers.
The prime factors with the smallest powers are 2² and 3¹

Step 4: Multiply these prime factors to get GCF of 36 and 48

GCF of 36 and 48 =  22 × 31 = 2 × 2 × 3 = 4 × 3 = 12

The Euclidean Algorithm method is used to determine the GCF of two numbers. In this method, the larger number is divided repeatedly by the smaller one and substituted by the larger number with the remainder. Continue this process until you get the remainder equal to zero. The last number before the remainder becomes zero is the GCF.

Go through the steps given below to find the GCF of 36 and 48 using the Euclidean Algorithm method:

• Firstly, divide the larger number by the smaller number:
• Divide 48 by 36, we get 12 as the remainder and the quotient as 1.
• Next, divide 36 by 12 giving 3 as the quotient and 0 as the remainder.
• Now, identify the last divisor before the remainder becomes 0. The GCF is the divisor at this point. Here, 12 is the divisor when the remainder becomes 0.

Therefore, the GCF of 36 and 48 using the Euclidean Algorithm is 12.
 

• Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

• Multiple: Multiples are the products we get by multiplying a given number with another. For example, the multiples of 4 are 4, 8, 12, 16, 20 and so on.

• Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 15 are 3 and 5.

• Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.