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

GCF of 8 and 36

GCF of 8 and 36 is the largest possible number that divides 8 and 36 exactly without any remainder. The factors of 8 and 36 are 1, 2, 4, 8 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 8 and 36 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 8 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 36?

Answer: GCF of 8 and 36 is 4.

Explanation:

The GCF of two non-zero integers, x(8) and y(36), is the greatest positive integer m(4) that divides both x(8) and y(36) without any remainder.

Methods to Find GCF of 8 and 36

Let's look at the different methods for finding the GCF of 8 and 36.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 8 and 36 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 3 common factors of 8 and 36, that are 1, 2, and 4. Therefore, the greatest common factor of 8 and 36 is 4.

GCF of 8 and 36 by Prime Factorization

Prime factorization of 8 and 36 is (2 × 2 × 2) and (2 × 2 × 3 × 3) respectively. As visible, 8 and 36 have common prime factors. Hence, the GCF of 8 and 36 is 2 × 2 = 4.

GCF of 8 and 36 by Long Division

GCF of 8 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 8 and 36.

☛ Also Check:

GCF of 8 and 36 Examples

Example 1: For two numbers, GCF = 4 and LCM = 72. If one number is 8, find the other number.

Solution:

Given: GCF (z, 8) = 4 and LCM (z, 8) = 72
∵ GCF × LCM = 8 × (z)
⇒ z = (GCF × LCM)/8
⇒ z = (4 × 72)/8
⇒ z = 36
Therefore, the other number is 36.
Example 2: Find the GCF of 8 and 36, if their LCM is 72.

Solution:

∵ LCM × GCF = 8 × 36
⇒ GCF(8, 36) = (8 × 36)/72 = 4
Therefore, the greatest common factor of 8 and 36 is 4.
Example 3: Find the greatest number that divides 8 and 36 exactly.

Solution:

The greatest number that divides 8 and 36 exactly is their greatest common factor, i.e. GCF of 8 and 36.
⇒ Factors of 8 and 36:
- Factors of 8 = 1, 2, 4, 8
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 8 and 36 is 4.

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 8 and 36

What is the GCF of 8 and 36?

The GCF of 8 and 36 is 4. To calculate the greatest common factor (GCF) of 8 and 36, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 8 and 36, i.e., 4.

If the GCF of 36 and 8 is 4, Find its LCM.

GCF(36, 8) × LCM(36, 8) = 36 × 8
Since the GCF of 36 and 8 = 4
⇒ 4 × LCM(36, 8) = 288
Therefore, LCM = 72
☛ GCF Calculator

How to Find the GCF of 8 and 36 by Prime Factorization?

To find the GCF of 8 and 36, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 8 and 36. Hence, GCF(8, 36) = 2 × 2 = 4
☛ Prime Number

What is the Relation Between LCM and GCF of 8, 36?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 8 and 36, i.e. GCF × LCM = 8 × 36.

What are the Methods to Find GCF of 8 and 36?

There are three commonly used methods to find the GCF of 8 and 36.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 8 and 36 by Long Division Method?

To find the GCF of 8, 36 using long division method, 36 is divided by 8. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum