A day full of math games & activities. Find one near you.

GCF of 36 and 63

GCF of 36 and 63 is the largest possible number that divides 36 and 63 exactly without any remainder. The factors of 36 and 63 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 36 and 63 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 36 and 63
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 63?

Answer: GCF of 36 and 63 is 9.

Explanation:

The GCF of two non-zero integers, x(36) and y(63), is the greatest positive integer m(9) that divides both x(36) and y(63) without any remainder.

Methods to Find GCF of 36 and 63

Let's look at the different methods for finding the GCF of 36 and 63.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

GCF of 36 and 63 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 63 and Y = 36

GCF(63, 36) = GCF(36, 63 mod 36) = GCF(36, 27)
GCF(36, 27) = GCF(27, 36 mod 27) = GCF(27, 9)
GCF(27, 9) = GCF(9, 27 mod 9) = GCF(9, 0)
GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 63 is 9.

GCF of 36 and 63 by Prime Factorization

Prime factorization of 36 and 63 is (2 × 2 × 3 × 3) and (3 × 3 × 7) respectively. As visible, 36 and 63 have common prime factors. Hence, the GCF of 36 and 63 is 3 × 3 = 9.

GCF of 36 and 63 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 63: 1, 3, 7, 9, 21, 63

There are 3 common factors of 36 and 63, that are 1, 3, and 9. Therefore, the greatest common factor of 36 and 63 is 9.

☛ Also Check:

GCF of 36 and 63 Examples

Example 1: The product of two numbers is 2268. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 2268
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2268/9
Therefore, the LCM is 252.
Example 2: For two numbers, GCF = 9 and LCM = 252. If one number is 36, find the other number.

Solution:

Given: GCF (x, 36) = 9 and LCM (x, 36) = 252
∵ GCF × LCM = 36 × (x)
⇒ x = (GCF × LCM)/36
⇒ x = (9 × 252)/36
⇒ x = 63
Therefore, the other number is 63.
Example 3: Find the greatest number that divides 36 and 63 exactly.

Solution:

The greatest number that divides 36 and 63 exactly is their greatest common factor, i.e. GCF of 36 and 63.
⇒ Factors of 36 and 63:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 63 = 1, 3, 7, 9, 21, 63
Therefore, the GCF of 36 and 63 is 9.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 36 and 63

What is the GCF of 36 and 63?

The GCF of 36 and 63 is 9. To calculate the GCF of 36 and 63, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 36 and 63, i.e., 9.

How to Find the GCF of 36 and 63 by Prime Factorization?

To find the GCF of 36 and 63, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 63 = 3 × 3 × 7.
⇒ Since 3, 3 are common terms in the prime factorization of 36 and 63. Hence, GCF(36, 63) = 3 × 3 = 9
☛ Prime Number

What is the Relation Between LCM and GCF of 36, 63?

The following equation can be used to express the relation between LCM and GCF of 36 and 63, i.e. GCF × LCM = 36 × 63.

What are the Methods to Find GCF of 36 and 63?

There are three commonly used methods to find the GCF of 36 and 63.

By Listing Common Factors
By Long Division
By Prime Factorization

If the GCF of 63 and 36 is 9, Find its LCM.

GCF(63, 36) × LCM(63, 36) = 63 × 36
Since the GCF of 63 and 36 = 9
⇒ 9 × LCM(63, 36) = 2268
Therefore, LCM = 252
☛ GCF Calculator

How to Find the GCF of 36 and 63 by Long Division Method?

To find the GCF of 36, 63 using long division method, 63 is divided by 36. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum