GCF of 18 and 33
GCF of 18 and 33 is the largest possible number that divides 18 and 33 exactly without any remainder. The factors of 18 and 33 are 1, 2, 3, 6, 9, 18 and 1, 3, 11, 33 respectively. There are 3 commonly used methods to find the GCF of 18 and 33 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 18 and 33 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 33?
Answer: GCF of 18 and 33 is 3.
Explanation:
The GCF of two non-zero integers, x(18) and y(33), is the greatest positive integer m(3) that divides both x(18) and y(33) without any remainder.
Methods to Find GCF of 18 and 33
Let's look at the different methods for finding the GCF of 18 and 33.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 18 and 33 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 33: 1, 3, 11, 33
There are 2 common factors of 18 and 33, that are 1 and 3. Therefore, the greatest common factor of 18 and 33 is 3.
GCF of 18 and 33 by Long Division
GCF of 18 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 18 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (15).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (3) is the GCF of 18 and 33.
GCF of 18 and 33 by Prime Factorization
Prime factorization of 18 and 33 is (2 × 3 × 3) and (3 × 11) respectively. As visible, 18 and 33 have only one common prime factor i.e. 3. Hence, the GCF of 18 and 33 is 3.
☛ Also Check:
- GCF of 75, 8 and 21 = 1
- GCF of 16 and 32 = 16
- GCF of 27 and 45 = 9
- GCF of 12 and 30 = 6
- GCF of 45 and 120 = 15
- GCF of 20 and 100 = 20
- GCF of 5 and 35 = 5
FAQs on GCF of 18 and 33
What is the GCF of 18 and 33?
The GCF of 18 and 33 is 3. To calculate the greatest common factor of 18 and 33, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 33 = 1, 3, 11, 33) and choose the greatest factor that exactly divides both 18 and 33, i.e., 3.
If the GCF of 33 and 18 is 3, Find its LCM.
GCF(33, 18) × LCM(33, 18) = 33 × 18
Since the GCF of 33 and 18 = 3
⇒ 3 × LCM(33, 18) = 594
Therefore, LCM = 198
☛ GCF Calculator
What is the Relation Between LCM and GCF of 18, 33?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 18 and 33, i.e. GCF × LCM = 18 × 33.
How to Find the GCF of 18 and 33 by Prime Factorization?
To find the GCF of 18 and 33, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 33 = 3 × 11.
⇒ Since 3 is the only common prime factor of 18 and 33. Hence, GCF (18, 33) = 3.
☛ What is a Prime Number?
How to Find the GCF of 18 and 33 by Long Division Method?
To find the GCF of 18, 33 using long division method, 33 is divided by 18. The corresponding divisor (3) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 18 and 33?
There are three commonly used methods to find the GCF of 18 and 33.
- By Prime Factorization
- By Long Division
- By Euclidean Algorithm