GCF of 42 and 72
GCF of 42 and 72 is the largest possible number that divides 42 and 72 exactly without any remainder. The factors of 42 and 72 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the GCF of 42 and 72 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 42 and 72 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 72?
Answer: GCF of 42 and 72 is 6
Explanation:
The GCF of two non-zero integers, x(42) and y(72), is the greatest positive integer m(6) that divides both x(42) and y(72) without any remainder.
Methods to Find GCF of 42 and 72
The methods to find the GCF of 42 and 72 are explained below.
- Using Euclid's Algorithm
- Long Division Method
- Prime Factorization Method
GCF of 42 and 72 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 = 72 and Y = 42
- GCF(72, 42) = GCF(42, 72 mod 42) = GCF(42, 30)
- GCF(42, 30) = GCF(30, 42 mod 30) = GCF(30, 12)
- GCF(30, 12) = GCF(12, 30 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 72 is 6.
GCF of 42 and 72 by Long Division
GCF of 42 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 72 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (30).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 42 and 72.
GCF of 42 and 72 by Prime Factorization
Prime factorization of 42 and 72 is (2 × 3 × 7) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 42 and 72 have common prime factors. Hence, the GCF of 42 and 72 is 2 × 3 = 6.
☛ Also Check:
- GCF of 48 and 120 = 24
- GCF of 39 and 65 = 13
- GCF of 7 and 35 = 7
- GCF of 20 and 30 = 10
- GCF of 26 and 39 = 13
- GCF of 63 and 72 = 9
- GCF of 28 and 70 = 14
FAQs on GCF of 42 and 72
What is the GCF of 42 and 72?
The GCF of 42 and 72 is 6. To calculate the GCF (Greatest Common Factor) of 42 and 72, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 42 and 72, i.e., 6.
What are the Methods to Find GCF of 42 and 72?
There are three commonly used methods to find the GCF of 42 and 72.
- By Long Division
- By Prime Factorization
- By Listing Common Factors
What is the Relation Between LCM and GCF of 42, 72?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 42 and 72, i.e. GCF × LCM = 42 × 72.
How to Find the GCF of 42 and 72 by Long Division Method?
To find the GCF of 42, 72 using long division method, 72 is divided by 42. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
How to Find the GCF of 42 and 72 by Prime Factorization?
To find the GCF of 42 and 72, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 42 and 72. Hence, GCF(42, 72) = 2 × 3 = 6
☛ What are Prime Numbers?
If the GCF of 72 and 42 is 6, Find its LCM.
GCF(72, 42) × LCM(72, 42) = 72 × 42
Since the GCF of 72 and 42 = 6
⇒ 6 × LCM(72, 42) = 3024
Therefore, LCM = 504
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