GCF of 42 and 86
GCF of 42 and 86 is the largest possible number that divides 42 and 86 exactly without any remainder. The factors of 42 and 86 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 43, 86 respectively. There are 3 commonly used methods to find the GCF of 42 and 86 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 42 and 86 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 86?
Answer: GCF of 42 and 86 is 2.
Explanation:
The GCF of two non-zero integers, x(42) and y(86), is the greatest positive integer m(2) that divides both x(42) and y(86) without any remainder.
Methods to Find GCF of 42 and 86
The methods to find the GCF of 42 and 86 are explained below.
- Listing Common Factors
- Long Division Method
- Using Euclid's Algorithm
GCF of 42 and 86 by Listing Common Factors
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 86: 1, 2, 43, 86
There are 2 common factors of 42 and 86, that are 1 and 2. Therefore, the greatest common factor of 42 and 86 is 2.
GCF of 42 and 86 by Long Division
GCF of 42 and 86 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 86 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (2).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (2) is the GCF of 42 and 86.
GCF of 42 and 86 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 = 86 and Y = 42
- GCF(86, 42) = GCF(42, 86 mod 42) = GCF(42, 2)
- GCF(42, 2) = GCF(2, 42 mod 2) = GCF(2, 0)
- GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 42 and 86 is 2.
☛ Also Check:
- GCF of 4 and 6 = 2
- GCF of 25 and 75 = 25
- GCF of 6 and 18 = 6
- GCF of 30 and 75 = 15
- GCF of 64 and 32 = 32
- GCF of 72 and 36 = 36
- GCF of 54 and 72 = 18
FAQs on GCF of 42 and 86
What is the GCF of 42 and 86?
The GCF of 42 and 86 is 2. To calculate the GCF of 42 and 86, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 86 = 1, 2, 43, 86) and choose the greatest factor that exactly divides both 42 and 86, i.e., 2.
If the GCF of 86 and 42 is 2, Find its LCM.
GCF(86, 42) × LCM(86, 42) = 86 × 42
Since the GCF of 86 and 42 = 2
⇒ 2 × LCM(86, 42) = 3612
Therefore, LCM = 1806
☛ GCF Calculator
What are the Methods to Find GCF of 42 and 86?
There are three commonly used methods to find the GCF of 42 and 86.
- By Euclidean Algorithm
- By Prime Factorization
- By Long Division
How to Find the GCF of 42 and 86 by Long Division Method?
To find the GCF of 42, 86 using long division method, 86 is divided by 42. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
How to Find the GCF of 42 and 86 by Prime Factorization?
To find the GCF of 42 and 86, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 86 = 2 × 43.
⇒ Since 2 is the only common prime factor of 42 and 86. Hence, GCF (42, 86) = 2.
☛ What are Prime Numbers?
What is the Relation Between LCM and GCF of 42, 86?
The following equation can be used to express the relation between Least Common Multiple and GCF of 42 and 86, i.e. GCF × LCM = 42 × 86.