GCF of 28 and 42
GCF of 28 and 42 is the largest possible number that divides 28 and 42 exactly without any remainder. The factors of 28 and 42 are 1, 2, 4, 7, 14, 28 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 28 and 42 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 28 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 28 and 42?
Answer: GCF of 28 and 42 is 14.
Explanation:
The GCF of two non-zero integers, x(28) and y(42), is the greatest positive integer m(14) that divides both x(28) and y(42) without any remainder.
Methods to Find GCF of 28 and 42
The methods to find the GCF of 28 and 42 are explained below.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 28 and 42 by Listing Common Factors
- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 28 and 42, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 28 and 42 is 14.
GCF of 28 and 42 by Long Division
GCF of 28 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 28 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (14).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (14) is the GCF of 28 and 42.
GCF of 28 and 42 by Prime Factorization
Prime factorization of 28 and 42 is (2 × 2 × 7) and (2 × 3 × 7) respectively. As visible, 28 and 42 have common prime factors. Hence, the GCF of 28 and 42 is 2 × 7 = 14.
☛ Also Check:
- GCF of 35 and 63 = 7
- GCF of 7 and 14 = 7
- GCF of 14 and 49 = 7
- GCF of 28 and 49 = 7
- GCF of 35 and 50 = 5
- GCF of 12 and 14 = 2
- GCF of 26 and 52 = 26
FAQs on GCF of 28 and 42
What is the GCF of 28 and 42?
The GCF of 28 and 42 is 14. To calculate the greatest common factor (GCF) of 28 and 42, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 28 and 42, i.e., 14.
How to Find the GCF of 28 and 42 by Long Division Method?
To find the GCF of 28, 42 using long division method, 42 is divided by 28. The corresponding divisor (14) when remainder equals 0 is taken as GCF.
If the GCF of 42 and 28 is 14, Find its LCM.
GCF(42, 28) × LCM(42, 28) = 42 × 28
Since the GCF of 42 and 28 = 14
⇒ 14 × LCM(42, 28) = 1176
Therefore, LCM = 84
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 28, 42?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 28 and 42, i.e. GCF × LCM = 28 × 42.
How to Find the GCF of 28 and 42 by Prime Factorization?
To find the GCF of 28 and 42, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 42 = 2 × 3 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 28 and 42. Hence, GCF(28, 42) = 2 × 7 = 14
☛ Prime Number
What are the Methods to Find GCF of 28 and 42?
There are three commonly used methods to find the GCF of 28 and 42.
- By Listing Common Factors
- By Prime Factorization
- By Long Division