GCF of 49 and 84
GCF of 49 and 84 is the largest possible number that divides 49 and 84 exactly without any remainder. The factors of 49 and 84 are 1, 7, 49 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 49 and 84 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 49 and 84 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 49 and 84?
Answer: GCF of 49 and 84 is 7.
Explanation:
The GCF of two non-zero integers, x(49) and y(84), is the greatest positive integer m(7) that divides both x(49) and y(84) without any remainder.
Methods to Find GCF of 49 and 84
Let's look at the different methods for finding the GCF of 49 and 84.
- Using Euclid's Algorithm
- Long Division Method
- Prime Factorization Method
GCF of 49 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 = 49
- GCF(84, 49) = GCF(49, 84 mod 49) = GCF(49, 35)
- GCF(49, 35) = GCF(35, 49 mod 35) = GCF(35, 14)
- GCF(35, 14) = GCF(14, 35 mod 14) = GCF(14, 7)
- GCF(14, 7) = GCF(7, 14 mod 7) = GCF(7, 0)
- GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 49 and 84 is 7.
GCF of 49 and 84 by Long Division
GCF of 49 and 84 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 84 (larger number) by 49 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (49) by the remainder (35).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (7) is the GCF of 49 and 84.
GCF of 49 and 84 by Prime Factorization
Prime factorization of 49 and 84 is (7 × 7) and (2 × 2 × 3 × 7) respectively. As visible, 49 and 84 have only one common prime factor i.e. 7. Hence, the GCF of 49 and 84 is 7.
☛ Also Check:
- GCF of 12 and 30 = 6
- GCF of 32 and 60 = 4
- GCF of 6 and 15 = 3
- GCF of 28 and 49 = 7
- GCF of 8 and 12 = 4
- GCF of 18 and 36 = 18
- GCF of 40 and 50 = 10
FAQs on GCF of 49 and 84
What is the GCF of 49 and 84?
The GCF of 49 and 84 is 7. To calculate the greatest common factor (GCF) of 49 and 84, we need to factor each number (factors of 49 = 1, 7, 49; factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and choose the greatest factor that exactly divides both 49 and 84, i.e., 7.
How to Find the GCF of 49 and 84 by Prime Factorization?
To find the GCF of 49 and 84, we will find the prime factorization of the given numbers, i.e. 49 = 7 × 7; 84 = 2 × 2 × 3 × 7.
⇒ Since 7 is the only common prime factor of 49 and 84. Hence, GCF (49, 84) = 7.
☛ Prime Number
If the GCF of 84 and 49 is 7, Find its LCM.
GCF(84, 49) × LCM(84, 49) = 84 × 49
Since the GCF of 84 and 49 = 7
⇒ 7 × LCM(84, 49) = 4116
Therefore, LCM = 588
☛ Greatest Common Factor Calculator
How to Find the GCF of 49 and 84 by Long Division Method?
To find the GCF of 49, 84 using long division method, 84 is divided by 49. The corresponding divisor (7) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 49, 84?
The following equation can be used to express the relation between LCM and GCF of 49 and 84, i.e. GCF × LCM = 49 × 84.
What are the Methods to Find GCF of 49 and 84?
There are three commonly used methods to find the GCF of 49 and 84.
- By Long Division
- By Listing Common Factors
- By Prime Factorization