GCF of 42 and 66
GCF of 42 and 66 is the largest possible number that divides 42 and 66 exactly without any remainder. The factors of 42 and 66 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 3, 6, 11, 22, 33, 66 respectively. There are 3 commonly used methods to find the GCF of 42 and 66 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 42 and 66 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 66?
Answer: GCF of 42 and 66 is 6.
Explanation:
The GCF of two non-zero integers, x(42) and y(66), is the greatest positive integer m(6) that divides both x(42) and y(66) without any remainder.
Methods to Find GCF of 42 and 66
The methods to find the GCF of 42 and 66 are explained below.
- Listing Common Factors
- Long Division Method
- Using Euclid's Algorithm
GCF of 42 and 66 by Listing Common Factors
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
There are 4 common factors of 42 and 66, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 42 and 66 is 6.
GCF of 42 and 66 by Long Division
GCF of 42 and 66 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 66 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (24).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 42 and 66.
GCF of 42 and 66 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 = 66 and Y = 42
- GCF(66, 42) = GCF(42, 66 mod 42) = GCF(42, 24)
- GCF(42, 24) = GCF(24, 42 mod 24) = GCF(24, 18)
- GCF(24, 18) = GCF(18, 24 mod 18) = GCF(18, 6)
- GCF(18, 6) = GCF(6, 18 mod 6) = GCF(6, 0)
- GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 42 and 66 is 6.
☛ Also Check:
- GCF of 49 and 63 = 7
- GCF of 14 and 16 = 2
- GCF of 72 and 120 = 24
- GCF of 75, 8 and 21 = 1
- GCF of 56 and 72 = 8
- GCF of 32 and 45 = 1
- GCF of 20 and 50 = 10
FAQs on GCF of 42 and 66
What is the GCF of 42 and 66?
The GCF of 42 and 66 is 6. To calculate the greatest common factor (GCF) of 42 and 66, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66) and choose the greatest factor that exactly divides both 42 and 66, i.e., 6.
What are the Methods to Find GCF of 42 and 66?
There are three commonly used methods to find the GCF of 42 and 66.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
How to Find the GCF of 42 and 66 by Prime Factorization?
To find the GCF of 42 and 66, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 66 = 2 × 3 × 11.
⇒ Since 2, 3 are common terms in the prime factorization of 42 and 66. Hence, GCF(42, 66) = 2 × 3 = 6
☛ What is a Prime Number?
What is the Relation Between LCM and GCF of 42, 66?
The following equation can be used to express the relation between Least Common Multiple and GCF of 42 and 66, i.e. GCF × LCM = 42 × 66.
How to Find the GCF of 42 and 66 by Long Division Method?
To find the GCF of 42, 66 using long division method, 66 is divided by 42. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
If the GCF of 66 and 42 is 6, Find its LCM.
GCF(66, 42) × LCM(66, 42) = 66 × 42
Since the GCF of 66 and 42 = 6
⇒ 6 × LCM(66, 42) = 2772
Therefore, LCM = 462
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