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GCF of 33 and 77

GCF of 33 and 77 is the largest possible number that divides 33 and 77 exactly without any remainder. The factors of 33 and 77 are 1, 3, 11, 33 and 1, 7, 11, 77 respectively. There are 3 commonly used methods to find the GCF of 33 and 77 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 33 and 77
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 33 and 77?

Answer: GCF of 33 and 77 is 11.

Explanation:

The GCF of two non-zero integers, x(33) and y(77), is the greatest positive integer m(11) that divides both x(33) and y(77) without any remainder.

Methods to Find GCF of 33 and 77

Let's look at the different methods for finding the GCF of 33 and 77.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 33 and 77 by Long Division

GCF of 33 and 77 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 77 (larger number) by 33 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (33) by the remainder (11).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (11) is the GCF of 33 and 77.

GCF of 33 and 77 by Listing Common Factors

Factors of 33: 1, 3, 11, 33
Factors of 77: 1, 7, 11, 77

There are 2 common factors of 33 and 77, that are 1 and 11. Therefore, the greatest common factor of 33 and 77 is 11.

GCF of 33 and 77 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 = 77 and Y = 33

GCF(77, 33) = GCF(33, 77 mod 33) = GCF(33, 11)
GCF(33, 11) = GCF(11, 33 mod 11) = GCF(11, 0)
GCF(11, 0) = 11 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 33 and 77 is 11.

☛ Also Check:

GCF of 33 and 77 Examples

Example 1: Find the GCF of 33 and 77, if their LCM is 231.

Solution:

∵ LCM × GCF = 33 × 77
⇒ GCF(33, 77) = (33 × 77)/231 = 11
Therefore, the greatest common factor of 33 and 77 is 11.
Example 2: Find the greatest number that divides 33 and 77 exactly.

Solution:

The greatest number that divides 33 and 77 exactly is their greatest common factor, i.e. GCF of 33 and 77.
⇒ Factors of 33 and 77:
- Factors of 33 = 1, 3, 11, 33
- Factors of 77 = 1, 7, 11, 77
Therefore, the GCF of 33 and 77 is 11.
Example 3: The product of two numbers is 2541. If their GCF is 11, what is their LCM?

Solution:

Given: GCF = 11 and product of numbers = 2541
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2541/11
Therefore, the LCM is 231.

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FAQs on GCF of 33 and 77

What is the GCF of 33 and 77?

The GCF of 33 and 77 is 11. To calculate the greatest common factor (GCF) of 33 and 77, we need to factor each number (factors of 33 = 1, 3, 11, 33; factors of 77 = 1, 7, 11, 77) and choose the greatest factor that exactly divides both 33 and 77, i.e., 11.

How to Find the GCF of 33 and 77 by Prime Factorization?

To find the GCF of 33 and 77, we will find the prime factorization of the given numbers, i.e. 33 = 3 × 11; 77 = 7 × 11.
⇒ Since 11 is the only common prime factor of 33 and 77. Hence, GCF (33, 77) = 11.
☛ Prime Numbers

What is the Relation Between LCM and GCF of 33, 77?

The following equation can be used to express the relation between LCM and GCF of 33 and 77, i.e. GCF × LCM = 33 × 77.

What are the Methods to Find GCF of 33 and 77?

There are three commonly used methods to find the GCF of 33 and 77.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 33 and 77 by Long Division Method?

To find the GCF of 33, 77 using long division method, 77 is divided by 33. The corresponding divisor (11) when remainder equals 0 is taken as GCF.

If the GCF of 77 and 33 is 11, Find its LCM.

GCF(77, 33) × LCM(77, 33) = 77 × 33
Since the GCF of 77 and 33 = 11
⇒ 11 × LCM(77, 33) = 2541
Therefore, LCM = 231
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