GCF of 42 and 54
GCF of 42 and 54 is the largest possible number that divides 42 and 54 exactly without any remainder. The factors of 42 and 54 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There are 3 commonly used methods to find the GCF of 42 and 54 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 42 and 54 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 54?
Answer: GCF of 42 and 54 is 6.
Explanation:
The GCF of two non-zero integers, x(42) and y(54), is the greatest positive integer m(6) that divides both x(42) and y(54) without any remainder.
Methods to Find GCF of 42 and 54
The methods to find the GCF of 42 and 54 are explained below.
- Using Euclid's Algorithm
- Long Division Method
- Prime Factorization Method
GCF of 42 and 54 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 = 54 and Y = 42
- GCF(54, 42) = GCF(42, 54 mod 42) = GCF(42, 12)
- GCF(42, 12) = GCF(12, 42 mod 12) = GCF(12, 6)
- GCF(12, 6) = GCF(6, 12 mod 6) = GCF(6, 0)
- GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 42 and 54 is 6.
GCF of 42 and 54 by Long Division
GCF of 42 and 54 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 54 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (12).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 42 and 54.
GCF of 42 and 54 by Prime Factorization
Prime factorization of 42 and 54 is (2 × 3 × 7) and (2 × 3 × 3 × 3) respectively. As visible, 42 and 54 have common prime factors. Hence, the GCF of 42 and 54 is 2 × 3 = 6.
☛ Also Check:
- GCF of 30 and 60 = 30
- GCF of 15 and 45 = 15
- GCF of 6 and 12 = 6
- GCF of 20 and 70 = 10
- GCF of 6 and 15 = 3
- GCF of 25 and 60 = 5
- GCF of 75 and 100 = 25
FAQs on GCF of 42 and 54
What is the GCF of 42 and 54?
The GCF of 42 and 54 is 6. To calculate the greatest common factor of 42 and 54, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and choose the greatest factor that exactly divides both 42 and 54, i.e., 6.
What are the Methods to Find GCF of 42 and 54?
There are three commonly used methods to find the GCF of 42 and 54.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
What is the Relation Between LCM and GCF of 42, 54?
The following equation can be used to express the relation between LCM and GCF of 42 and 54, i.e. GCF × LCM = 42 × 54.
If the GCF of 54 and 42 is 6, Find its LCM.
GCF(54, 42) × LCM(54, 42) = 54 × 42
Since the GCF of 54 and 42 = 6
⇒ 6 × LCM(54, 42) = 2268
Therefore, LCM = 378
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How to Find the GCF of 42 and 54 by Long Division Method?
To find the GCF of 42, 54 using long division method, 54 is divided by 42. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
How to Find the GCF of 42 and 54 by Prime Factorization?
To find the GCF of 42 and 54, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 54 = 2 × 3 × 3 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 42 and 54. Hence, GCF(42, 54) = 2 × 3 = 6
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