GCF of 86 and 42
GCF of 86 and 42 is the largest possible number that divides 86 and 42 exactly without any remainder. The factors of 86 and 42 are 1, 2, 43, 86 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 86 and 42 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 86 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 86 and 42?
Answer: GCF of 86 and 42 is 2.
Explanation:
The GCF of two non-zero integers, x(86) and y(42), is the greatest positive integer m(2) that divides both x(86) and y(42) without any remainder.
Methods to Find GCF of 86 and 42
The methods to find the GCF of 86 and 42 are explained below.
- Listing Common Factors
- Using Euclid's Algorithm
- Long Division Method
GCF of 86 and 42 by Listing Common Factors
- Factors of 86: 1, 2, 43, 86
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 2 common factors of 86 and 42, that are 1 and 2. Therefore, the greatest common factor of 86 and 42 is 2.
GCF of 86 and 42 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 86 and 42 is 2.
GCF of 86 and 42 by Long Division
GCF of 86 and 42 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 86 and 42.
☛ Also Check:
- GCF of 32 and 36 = 4
- GCF of 15 and 75 = 15
- GCF of 72 and 81 = 9
- GCF of 36 and 54 = 18
- GCF of 12 and 18 = 6
- GCF of 25 and 55 = 5
- GCF of 36 and 84 = 12
FAQs on GCF of 86 and 42
What is the GCF of 86 and 42?
The GCF of 86 and 42 is 2. To calculate the GCF (Greatest Common Factor) of 86 and 42, we need to factor each number (factors of 86 = 1, 2, 43, 86; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 86 and 42, i.e., 2.
How to Find the GCF of 86 and 42 by Prime Factorization?
To find the GCF of 86 and 42, we will find the prime factorization of the given numbers, i.e. 86 = 2 × 43; 42 = 2 × 3 × 7.
⇒ Since 2 is the only common prime factor of 86 and 42. Hence, GCF (86, 42) = 2.
☛ What is a Prime Number?
How to Find the GCF of 86 and 42 by Long Division Method?
To find the GCF of 86, 42 using long division method, 86 is divided by 42. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
If the GCF of 42 and 86 is 2, Find its LCM.
GCF(42, 86) × LCM(42, 86) = 42 × 86
Since the GCF of 42 and 86 = 2
⇒ 2 × LCM(42, 86) = 3612
Therefore, LCM = 1806
☛ GCF Calculator
What is the Relation Between LCM and GCF of 86, 42?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 86 and 42, i.e. GCF × LCM = 86 × 42.
What are the Methods to Find GCF of 86 and 42?
There are three commonly used methods to find the GCF of 86 and 42.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division