GCF of 4 and 18 is the largest possible number that divides 4 and 18 exactly without any remainder. The factors of 4 and 18 are 1, 2, 4 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the GCF of 4 and 18 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 4 and 18 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 4 and 18?
Answer: GCF of 4 and 18 is 2.
Explanation:
The GCF of two non-zero integers, x(4) and y(18), is the greatest positive integer m(2) that divides both x(4) and y(18) without any remainder.
Methods to Find GCF of 4 and 18
Let's look at the different methods for finding the GCF of 4 and 18.
- Using Euclid's Algorithm
- Prime Factorization Method
- Long Division Method
GCF of 4 and 18 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 = 18 and Y = 4
- GCF(18, 4) = GCF(4, 18 mod 4) = GCF(4, 2)
- GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
- GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 4 and 18 is 2.
GCF of 4 and 18 by Prime Factorization
Prime factorization of 4 and 18 is (2 × 2) and (2 × 3 × 3) respectively. As visible, 4 and 18 have only one common prime factor i.e. 2. Hence, the GCF of 4 and 18 is 2.
GCF of 4 and 18 by Long Division
GCF of 4 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 18 (larger number) by 4 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4) by the remainder (2).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (2) is the GCF of 4 and 18.
☛ Also Check:
- GCF of 25 and 100 = 25
- GCF of 44 and 66 = 22
- GCF of 21 and 24 = 3
- GCF of 56 and 72 = 8
- GCF of 26 and 14 = 2
- GCF of 18 and 30 = 6
- GCF of 28 and 40 = 4
GCF of 4 and 18 Examples
Example 1: For two numbers, GCF = 2 and LCM = 36. If one number is 4, find the other number.
Solution:
Given: GCF (y, 4) = 2 and LCM (y, 4) = 36
∵ GCF × LCM = 4 × (y)
⇒ y = (GCF × LCM)/4
⇒ y = (2 × 36)/4
⇒ y = 18
Therefore, the other number is 18.Example 2: Find the GCF of 4 and 18, if their LCM is 36.
Solution:
∵ LCM × GCF = 4 × 18
⇒ GCF(4, 18) = (4 × 18)/36 = 2
Therefore, the greatest common factor of 4 and 18 is 2.Example 3: Find the greatest number that divides 4 and 18 exactly.
Solution:
The greatest number that divides 4 and 18 exactly is their greatest common factor, i.e. GCF of 4 and 18.
⇒ Factors of 4 and 18:- Factors of 4 = 1, 2, 4
- Factors of 18 = 1, 2, 3, 6, 9, 18
Therefore, the GCF of 4 and 18 is 2.
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FAQs on GCF of 4 and 18
What is the GCF of 4 and 18?
The GCF of 4 and 18 is 2. To calculate the greatest common factor (GCF) of 4 and 18, we need to factor each number (factors of 4 = 1, 2, 4; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the greatest factor that exactly divides both 4 and 18, i.e., 2.
How to Find the GCF of 4 and 18 by Prime Factorization?
To find the GCF of 4 and 18, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 18 = 2 × 3 × 3.
⇒ Since 2 is the only common prime factor of 4 and 18. Hence, GCF (4, 18) = 2.
☛ Prime Number
What are the Methods to Find GCF of 4 and 18?
There are three commonly used methods to find the GCF of 4 and 18.
- By Euclidean Algorithm
- By Long Division
- By Prime Factorization
If the GCF of 18 and 4 is 2, Find its LCM.
GCF(18, 4) × LCM(18, 4) = 18 × 4
Since the GCF of 18 and 4 = 2
⇒ 2 × LCM(18, 4) = 72
Therefore, LCM = 36
☛ Greatest Common Factor Calculator
How to Find the GCF of 4 and 18 by Long Division Method?
To find the GCF of 4, 18 using long division method, 18 is divided by 4. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 4, 18?
The following equation can be used to express the relation between LCM and GCF of 4 and 18, i.e. GCF × LCM = 4 × 18.
