GCF of 6 and 33
GCF of 6 and 33 is the largest possible number that divides 6 and 33 exactly without any remainder. The factors of 6 and 33 are 1, 2, 3, 6 and 1, 3, 11, 33 respectively. There are 3 commonly used methods to find the GCF of 6 and 33 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 6 and 33 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 6 and 33?
Answer: GCF of 6 and 33 is 3.
Explanation:
The GCF of two non-zero integers, x(6) and y(33), is the greatest positive integer m(3) that divides both x(6) and y(33) without any remainder.
Methods to Find GCF of 6 and 33
The methods to find the GCF of 6 and 33 are explained below.
- Using Euclid's Algorithm
- Long Division Method
- Listing Common Factors
GCF of 6 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 = 6
- GCF(33, 6) = GCF(6, 33 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 6 and 33 is 3.
GCF of 6 and 33 by Long Division
GCF of 6 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 6 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (3).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (3) is the GCF of 6 and 33.
GCF of 6 and 33 by Listing Common Factors
- Factors of 6: 1, 2, 3, 6
- Factors of 33: 1, 3, 11, 33
There are 2 common factors of 6 and 33, that are 1 and 3. Therefore, the greatest common factor of 6 and 33 is 3.
☛ Also Check:
- GCF of 90 and 27 = 9
- GCF of 6 and 7 = 1
- GCF of 28 and 32 = 4
- GCF of 16 and 60 = 4
- GCF of 12 and 56 = 4
- GCF of 32 and 56 = 8
- GCF of 63 and 72 = 9
FAQs on GCF of 6 and 33
What is the GCF of 6 and 33?
The GCF of 6 and 33 is 3. To calculate the GCF (Greatest Common Factor) of 6 and 33, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 33 = 1, 3, 11, 33) and choose the greatest factor that exactly divides both 6 and 33, i.e., 3.
How to Find the GCF of 6 and 33 by Prime Factorization?
To find the GCF of 6 and 33, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 33 = 3 × 11.
⇒ Since 3 is the only common prime factor of 6 and 33. Hence, GCF (6, 33) = 3.
☛ Prime Number
What are the Methods to Find GCF of 6 and 33?
There are three commonly used methods to find the GCF of 6 and 33.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
What is the Relation Between LCM and GCF of 6, 33?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 6 and 33, i.e. GCF × LCM = 6 × 33.
If the GCF of 33 and 6 is 3, Find its LCM.
GCF(33, 6) × LCM(33, 6) = 33 × 6
Since the GCF of 33 and 6 = 3
⇒ 3 × LCM(33, 6) = 198
Therefore, LCM = 66
☛ Greatest Common Factor Calculator
How to Find the GCF of 6 and 33 by Long Division Method?
To find the GCF of 6, 33 using long division method, 33 is divided by 6. The corresponding divisor (3) when remainder equals 0 is taken as GCF.