What is the GCF of 36 and 84?
GCF (Greatest Common Factor) of two numbers is the largest number that divides the two numbers exactly leaving the remainder 0
Answer: GCF of 36 and 84 is 12
Let us see how to find the GCF of 36 and 84
Explanation:
The greatest common factor of 36 and 84 is the greatest number which divides the numbers 36 and 84 exactly. We will use the two methods to find the GCF of 36 and 84
We can find the GCF by the following methods.

Greatest Common Factor of 36 and 84 by Prime Factorization

Greatest Common Factor of 36 and 84 by Long Division
Method 1: Greatest Common Factor of 36 and 84 by Prime Factorization
Let's write the prime factorization of 36 and 84
Prime factorization of 36 is 2 × 2 × 3 × 3
Prime factorization of 84 is 2 × 2 × 3 × 7
The common prime factors in the above prime factorization are 2, 2, and 3
The greatest common factor is the product of the prime factors that are common to each of the given numbers.
So, GCF of 36 and 84 is 2 × 2 × 3 = 12
Method 2: Greatest Common Factor of 36 and 84 by Long Division
Step 1: Divide 84 by 36 and check the remainder. Here, the remainder is 12
Step 2: Make the remainder 12 as the divisor and the divisor 36 as the dividend and perform the long division again.
Step 3: Continue till you get the remainder as 0 and the last divisor will be the GCF (36, 84)
The solution to our question GCF of 36 and 84 is the same by both the methods.