GCF of 24 and 42
GCF of 24 and 42 is the largest possible number that divides 24 and 42 exactly without any remainder. The factors of 24 and 42 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 24 and 42 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 24 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 24 and 42?
Answer: GCF of 24 and 42 is 6.
Explanation:
The GCF of two non-zero integers, x(24) and y(42), is the greatest positive integer m(6) that divides both x(24) and y(42) without any remainder.
Methods to Find GCF of 24 and 42
The methods to find the GCF of 24 and 42 are explained below.
- Long Division Method
- Listing Common Factors
- Prime Factorization Method
GCF of 24 and 42 by Long Division
GCF of 24 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 42 (larger number) by 24 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (18).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 24 and 42.
GCF of 24 and 42 by Listing Common Factors
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 24 and 42, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 24 and 42 is 6.
GCF of 24 and 42 by Prime Factorization
Prime factorization of 24 and 42 is (2 × 2 × 2 × 3) and (2 × 3 × 7) respectively. As visible, 24 and 42 have common prime factors. Hence, the GCF of 24 and 42 is 2 × 3 = 6.
☛ Also Check:
- GCF of 84 and 96 = 12
- GCF of 24 and 30 = 6
- GCF of 21 and 84 = 21
- GCF of 64 and 80 = 16
- GCF of 44, 12 and 28 = 4
- GCF of 4 and 12 = 4
- GCF of 35 and 42 = 7
FAQs on GCF of 24 and 42
What is the GCF of 24 and 42?
The GCF of 24 and 42 is 6. To calculate the greatest common factor (GCF) of 24 and 42, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 24 and 42, i.e., 6.
What is the Relation Between LCM and GCF of 24, 42?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 24 and 42, i.e. GCF × LCM = 24 × 42.
What are the Methods to Find GCF of 24 and 42?
There are three commonly used methods to find the GCF of 24 and 42.
- By Euclidean Algorithm
- By Prime Factorization
- By Long Division
How to Find the GCF of 24 and 42 by Prime Factorization?
To find the GCF of 24 and 42, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 24 and 42. Hence, GCF(24, 42) = 2 × 3 = 6
☛ Prime Numbers
How to Find the GCF of 24 and 42 by Long Division Method?
To find the GCF of 24, 42 using long division method, 42 is divided by 24. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
If the GCF of 42 and 24 is 6, Find its LCM.
GCF(42, 24) × LCM(42, 24) = 42 × 24
Since the GCF of 42 and 24 = 6
⇒ 6 × LCM(42, 24) = 1008
Therefore, LCM = 168
☛ Greatest Common Factor Calculator