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GCF of 36 and 49

GCF of 36 and 49 is the largest possible number that divides 36 and 49 exactly without any remainder. The factors of 36 and 49 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 7, 49 respectively. There are 3 commonly used methods to find the GCF of 36 and 49 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 36 and 49
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 49?

Answer: GCF of 36 and 49 is 1.

Explanation:

The GCF of two non-zero integers, x(36) and y(49), is the greatest positive integer m(1) that divides both x(36) and y(49) without any remainder.

Methods to Find GCF of 36 and 49

Let's look at the different methods for finding the GCF of 36 and 49.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 36 and 49 by Long Division

GCF of 36 and 49 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 49 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (13).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 36 and 49.

GCF of 36 and 49 by Prime Factorization

Prime factorization of 36 and 49 is (2 × 2 × 3 × 3) and (7 × 7) respectively. As visible, there are no common prime factors between 36 and 49, i.e. they are co-prime. Hence, the GCF of 36 and 49 will be 1.

GCF of 36 and 49 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 49: 1, 7, 49

Since, 1 is the only common factor between 36 and 49. The Greatest Common Factor of 36 and 49 is 1.

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GCF of 36 and 49 Examples

Example 1: Find the greatest number that divides 36 and 49 exactly.

Solution:

The greatest number that divides 36 and 49 exactly is their greatest common factor, i.e. GCF of 36 and 49.
⇒ Factors of 36 and 49:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 49 = 1, 7, 49
Therefore, the GCF of 36 and 49 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 1764. If one number is 49, find the other number.

Solution:

Given: GCF (y, 49) = 1 and LCM (y, 49) = 1764
∵ GCF × LCM = 49 × (y)
⇒ y = (GCF × LCM)/49
⇒ y = (1 × 1764)/49
⇒ y = 36
Therefore, the other number is 36.
Example 3: The product of two numbers is 1764. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 1764
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1764/1
Therefore, the LCM is 1764.

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FAQs on GCF of 36 and 49

What is the GCF of 36 and 49?

The GCF of 36 and 49 is 1. To calculate the greatest common factor of 36 and 49, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 49 = 1, 7, 49) and choose the greatest factor that exactly divides both 36 and 49, i.e., 1.

How to Find the GCF of 36 and 49 by Prime Factorization?

To find the GCF of 36 and 49, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 49 = 7 × 7.
⇒ There is no common prime factor for 36 and 49. Hence, GCF (36, 49) = 1.
☛ What is a Prime Number?

How to Find the GCF of 36 and 49 by Long Division Method?

To find the GCF of 36, 49 using long division method, 49 is divided by 36. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

If the GCF of 49 and 36 is 1, Find its LCM.

GCF(49, 36) × LCM(49, 36) = 49 × 36
Since the GCF of 49 and 36 = 1
⇒ 1 × LCM(49, 36) = 1764
Therefore, LCM = 1764
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 36, 49?

The following equation can be used to express the relation between LCM and GCF of 36 and 49, i.e. GCF × LCM = 36 × 49.

What are the Methods to Find GCF of 36 and 49?

There are three commonly used methods to find the GCF of 36 and 49.

By Listing Common Factors
By Prime Factorization
By Long Division

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