GCF of 14 and 84
GCF of 14 and 84 is the largest possible number that divides 14 and 84 exactly without any remainder. The factors of 14 and 84 are 1, 2, 7, 14 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 14 and 84 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 14 and 84 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 14 and 84?
Answer: GCF of 14 and 84 is 14.
Explanation:
The GCF of two non-zero integers, x(14) and y(84), is the greatest positive integer m(14) that divides both x(14) and y(84) without any remainder.
Methods to Find GCF of 14 and 84
Let's look at the different methods for finding the GCF of 14 and 84.
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 14 and 84 by Prime Factorization
Prime factorization of 14 and 84 is (2 × 7) and (2 × 2 × 3 × 7) respectively. As visible, 14 and 84 have common prime factors. Hence, the GCF of 14 and 84 is 2 × 7 = 14.
GCF of 14 and 84 by Long Division
GCF of 14 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 14 (smaller number).
- Step 2: Since the remainder = 0, the divisor (14) is the GCF of 14 and 84.
The corresponding divisor (14) is the GCF of 14 and 84.
GCF of 14 and 84 by Listing Common Factors
- Factors of 14: 1, 2, 7, 14
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
There are 4 common factors of 14 and 84, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 14 and 84 is 14.
☛ Also Check:
- GCF of 28 and 32 = 4
- GCF of 16 and 48 = 16
- GCF of 15 and 75 = 15
- GCF of 28 and 49 = 7
- GCF of 44 and 66 = 22
- GCF of 40 and 48 = 8
- GCF of 32 and 36 = 4
FAQs on GCF of 14 and 84
What is the GCF of 14 and 84?
The GCF of 14 and 84 is 14. To calculate the GCF (Greatest Common Factor) of 14 and 84, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and choose the greatest factor that exactly divides both 14 and 84, i.e., 14.
What are the Methods to Find GCF of 14 and 84?
There are three commonly used methods to find the GCF of 14 and 84.
- By Listing Common Factors
- By Long Division
- By Prime Factorization
How to Find the GCF of 14 and 84 by Long Division Method?
To find the GCF of 14, 84 using long division method, 84 is divided by 14. The corresponding divisor (14) when remainder equals 0 is taken as GCF.
How to Find the GCF of 14 and 84 by Prime Factorization?
To find the GCF of 14 and 84, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 84 = 2 × 2 × 3 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 14 and 84. Hence, GCF(14, 84) = 2 × 7 = 14
☛ What are Prime Numbers?
If the GCF of 84 and 14 is 14, Find its LCM.
GCF(84, 14) × LCM(84, 14) = 84 × 14
Since the GCF of 84 and 14 = 14
⇒ 14 × LCM(84, 14) = 1176
Therefore, LCM = 84
☛ GCF Calculator
What is the Relation Between LCM and GCF of 14, 84?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 14 and 84, i.e. GCF × LCM = 14 × 84.