GCF of 42 and 48
GCF of 42 and 48 is the largest possible number that divides 42 and 48 exactly without any remainder. The factors of 42 and 48 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 42 and 48 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 42 and 48 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 48?
Answer: GCF of 42 and 48 is 6.
Explanation:
The GCF of two non-zero integers, x(42) and y(48), is the greatest positive integer m(6) that divides both x(42) and y(48) without any remainder.
Methods to Find GCF of 42 and 48
Let's look at the different methods for finding the GCF of 42 and 48.
- Listing Common Factors
- Long Division Method
- Using Euclid's Algorithm
GCF of 42 and 48 by Listing Common Factors
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
There are 4 common factors of 42 and 48, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 42 and 48 is 6.
GCF of 42 and 48 by Long Division
GCF of 42 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 48 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (6).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 42 and 48.
GCF of 42 and 48 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 = 48 and Y = 42
- GCF(48, 42) = GCF(42, 48 mod 42) = GCF(42, 6)
- GCF(42, 6) = GCF(6, 42 mod 6) = GCF(6, 0)
- GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 42 and 48 is 6.
☛ Also Check:
- GCF of 84 and 42 = 42
- GCF of 15 and 50 = 5
- GCF of 24 and 96 = 24
- GCF of 39 and 6 = 3
- GCF of 18 and 30 = 6
- GCF of 20 and 32 = 4
- GCF of 2 and 5 = 1
FAQs on GCF of 42 and 48
What is the GCF of 42 and 48?
The GCF of 42 and 48 is 6. To calculate the greatest common factor of 42 and 48, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 42 and 48, i.e., 6.
How to Find the GCF of 42 and 48 by Long Division Method?
To find the GCF of 42, 48 using long division method, 48 is divided by 42. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 42 and 48?
There are three commonly used methods to find the GCF of 42 and 48.
- By Listing Common Factors
- By Long Division
- By Prime Factorization
How to Find the GCF of 42 and 48 by Prime Factorization?
To find the GCF of 42 and 48, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 42 and 48. Hence, GCF(42, 48) = 2 × 3 = 6
☛ What is a Prime Number?
What is the Relation Between LCM and GCF of 42, 48?
The following equation can be used to express the relation between LCM and GCF of 42 and 48, i.e. GCF × LCM = 42 × 48.
If the GCF of 48 and 42 is 6, Find its LCM.
GCF(48, 42) × LCM(48, 42) = 48 × 42
Since the GCF of 48 and 42 = 6
⇒ 6 × LCM(48, 42) = 2016
Therefore, LCM = 336
☛ Greatest Common Factor Calculator