GCF of 42 and 60
GCF of 42 and 60 is the largest possible number that divides 42 and 60 exactly without any remainder. The factors of 42 and 60 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There are 3 commonly used methods to find the GCF of 42 and 60 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 42 and 60 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 60?
Answer: GCF of 42 and 60 is 6.
Explanation:
The GCF of two non-zero integers, x(42) and y(60), is the greatest positive integer m(6) that divides both x(42) and y(60) without any remainder.
Methods to Find GCF of 42 and 60
The methods to find the GCF of 42 and 60 are explained below.
- Long Division Method
- Prime Factorization Method
- Listing Common Factors
GCF of 42 and 60 by Long Division
GCF of 42 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 60 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (18).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 42 and 60.
GCF of 42 and 60 by Prime Factorization
Prime factorization of 42 and 60 is (2 × 3 × 7) and (2 × 2 × 3 × 5) respectively. As visible, 42 and 60 have common prime factors. Hence, the GCF of 42 and 60 is 2 × 3 = 6.
GCF of 42 and 60 by Listing Common Factors
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
There are 4 common factors of 42 and 60, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 42 and 60 is 6.
☛ Also Check:
- GCF of 9 and 36 = 9
- GCF of 10 and 45 = 5
- GCF of 14 and 16 = 2
- GCF of 38 and 57 = 19
- GCF of 24 and 80 = 8
- GCF of 10 and 16 = 2
- GCF of 9 and 21 = 3
FAQs on GCF of 42 and 60
What is the GCF of 42 and 60?
The GCF of 42 and 60 is 6. To calculate the GCF of 42 and 60, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest factor that exactly divides both 42 and 60, i.e., 6.
If the GCF of 60 and 42 is 6, Find its LCM.
GCF(60, 42) × LCM(60, 42) = 60 × 42
Since the GCF of 60 and 42 = 6
⇒ 6 × LCM(60, 42) = 2520
Therefore, LCM = 420
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 42, 60?
The following equation can be used to express the relation between Least Common Multiple and GCF of 42 and 60, i.e. GCF × LCM = 42 × 60.
How to Find the GCF of 42 and 60 by Long Division Method?
To find the GCF of 42, 60 using long division method, 60 is divided by 42. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
How to Find the GCF of 42 and 60 by Prime Factorization?
To find the GCF of 42 and 60, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 42 and 60. Hence, GCF(42, 60) = 2 × 3 = 6
☛ Prime Number
What are the Methods to Find GCF of 42 and 60?
There are three commonly used methods to find the GCF of 42 and 60.
- By Euclidean Algorithm
- By Long Division
- By Prime Factorization