GCF of 48 and 84
GCF of 48 and 84 is the largest possible number that divides 48 and 84 exactly without any remainder. The factors of 48 and 84 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 respectively. There are 3 commonly used methods to find the GCF of 48 and 84 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 48 and 84 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 48 and 84?
Answer: GCF of 48 and 84 is 12.
Explanation:
The GCF of two non-zero integers, x(48) and y(84), is the greatest positive integer m(12) that divides both x(48) and y(84) without any remainder.
Methods to Find GCF of 48 and 84
Let's look at the different methods for finding the GCF of 48 and 84.
- Listing Common Factors
- Using Euclid's Algorithm
- Prime Factorization Method
GCF of 48 and 84 by Listing Common Factors
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
There are 6 common factors of 48 and 84, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 48 and 84 is 12.
GCF of 48 and 84 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 = 84 and Y = 48
- GCF(84, 48) = GCF(48, 84 mod 48) = GCF(48, 36)
- GCF(48, 36) = GCF(36, 48 mod 36) = GCF(36, 12)
- GCF(36, 12) = GCF(12, 36 mod 12) = GCF(12, 0)
- GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 48 and 84 is 12.
GCF of 48 and 84 by Prime Factorization
Prime factorization of 48 and 84 is (2 × 2 × 2 × 2 × 3) and (2 × 2 × 3 × 7) respectively. As visible, 48 and 84 have common prime factors. Hence, the GCF of 48 and 84 is 2 × 2 × 3 = 12.
☛ Also Check:
- GCF of 16 and 48 = 16
- GCF of 25 and 40 = 5
- GCF of 18 and 27 = 9
- GCF of 28 and 70 = 14
- GCF of 25 and 60 = 5
- GCF of 6 and 18 = 6
- GCF of 8 and 20 = 4
FAQs on GCF of 48 and 84
What is the GCF of 48 and 84?
The GCF of 48 and 84 is 12. To calculate the GCF (Greatest Common Factor) of 48 and 84, we need to factor each number (factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and choose the greatest factor that exactly divides both 48 and 84, i.e., 12.
How to Find the GCF of 48 and 84 by Long Division Method?
To find the GCF of 48, 84 using long division method, 84 is divided by 48. The corresponding divisor (12) when remainder equals 0 is taken as GCF.
How to Find the GCF of 48 and 84 by Prime Factorization?
To find the GCF of 48 and 84, we will find the prime factorization of the given numbers, i.e. 48 = 2 × 2 × 2 × 2 × 3; 84 = 2 × 2 × 3 × 7.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 48 and 84. Hence, GCF(48, 84) = 2 × 2 × 3 = 12
☛ Prime Numbers
If the GCF of 84 and 48 is 12, Find its LCM.
GCF(84, 48) × LCM(84, 48) = 84 × 48
Since the GCF of 84 and 48 = 12
⇒ 12 × LCM(84, 48) = 4032
Therefore, LCM = 336
☛ Greatest Common Factor Calculator
What are the Methods to Find GCF of 48 and 84?
There are three commonly used methods to find the GCF of 48 and 84.
- By Long Division
- By Prime Factorization
- By Euclidean Algorithm
What is the Relation Between LCM and GCF of 48, 84?
The following equation can be used to express the relation between Least Common Multiple and GCF of 48 and 84, i.e. GCF × LCM = 48 × 84.