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GCF of 24 and 33

GCF of 24 and 33 is the largest possible number that divides 24 and 33 exactly without any remainder. The factors of 24 and 33 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 3, 11, 33 respectively. There are 3 commonly used methods to find the GCF of 24 and 33 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 24 and 33
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 33?

Answer: GCF of 24 and 33 is 3.

Explanation:

The GCF of two non-zero integers, x(24) and y(33), is the greatest positive integer m(3) that divides both x(24) and y(33) without any remainder.

Methods to Find GCF of 24 and 33

The methods to find the GCF of 24 and 33 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 24 and 33 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 = 33 and Y = 24

GCF(33, 24) = GCF(24, 33 mod 24) = GCF(24, 9)
GCF(24, 9) = GCF(9, 24 mod 9) = GCF(9, 6)
GCF(9, 6) = GCF(6, 9 mod 6) = GCF(6, 3)
GCF(6, 3) = GCF(3, 6 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 24 and 33 is 3.

GCF of 24 and 33 by Prime Factorization

Prime factorization of 24 and 33 is (2 × 2 × 2 × 3) and (3 × 11) respectively. As visible, 24 and 33 have only one common prime factor i.e. 3. Hence, the GCF of 24 and 33 is 3.

GCF of 24 and 33 by Long Division

GCF of 24 and 33 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 33 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 24 and 33.

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GCF of 24 and 33 Examples

Example 1: The product of two numbers is 792. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 792
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 792/3
Therefore, the LCM is 264.
Example 2: Find the GCF of 24 and 33, if their LCM is 264.

Solution:

∵ LCM × GCF = 24 × 33
⇒ GCF(24, 33) = (24 × 33)/264 = 3
Therefore, the greatest common factor of 24 and 33 is 3.
Example 3: Find the greatest number that divides 24 and 33 exactly.

Solution:

The greatest number that divides 24 and 33 exactly is their greatest common factor, i.e. GCF of 24 and 33.
⇒ Factors of 24 and 33:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 33 = 1, 3, 11, 33
Therefore, the GCF of 24 and 33 is 3.

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FAQs on GCF of 24 and 33

What is the GCF of 24 and 33?

The GCF of 24 and 33 is 3. To calculate the GCF (Greatest Common Factor) of 24 and 33, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 33 = 1, 3, 11, 33) and choose the greatest factor that exactly divides both 24 and 33, i.e., 3.

If the GCF of 33 and 24 is 3, Find its LCM.

GCF(33, 24) × LCM(33, 24) = 33 × 24
Since the GCF of 33 and 24 = 3
⇒ 3 × LCM(33, 24) = 792
Therefore, LCM = 264
☛ Greatest Common Factor Calculator

How to Find the GCF of 24 and 33 by Long Division Method?

To find the GCF of 24, 33 using long division method, 33 is divided by 24. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

How to Find the GCF of 24 and 33 by Prime Factorization?

To find the GCF of 24 and 33, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 33 = 3 × 11.
⇒ Since 3 is the only common prime factor of 24 and 33. Hence, GCF (24, 33) = 3.
☛ What are Prime Numbers?

What are the Methods to Find GCF of 24 and 33?

There are three commonly used methods to find the GCF of 24 and 33.

By Prime Factorization
By Euclidean Algorithm
By Long Division

What is the Relation Between LCM and GCF of 24, 33?

The following equation can be used to express the relation between LCM and GCF of 24 and 33, i.e. GCF × LCM = 24 × 33.

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