GCF of 84 and 105
GCF of 84 and 105 is the largest possible number that divides 84 and 105 exactly without any remainder. The factors of 84 and 105 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and 1, 3, 5, 7, 15, 21, 35, 105 respectively. There are 3 commonly used methods to find the GCF of 84 and 105 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 84 and 105 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 84 and 105?
Answer: GCF of 84 and 105 is 21.
Explanation:
The GCF of two non-zero integers, x(84) and y(105), is the greatest positive integer m(21) that divides both x(84) and y(105) without any remainder.
Methods to Find GCF of 84 and 105
The methods to find the GCF of 84 and 105 are explained below.
- Long Division Method
- Listing Common Factors
- Prime Factorization Method
GCF of 84 and 105 by Long Division
GCF of 84 and 105 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 105 (larger number) by 84 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (84) by the remainder (21).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (21) is the GCF of 84 and 105.
GCF of 84 and 105 by Listing Common Factors
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
There are 4 common factors of 84 and 105, that are 1, 3, 21, and 7. Therefore, the greatest common factor of 84 and 105 is 21.
GCF of 84 and 105 by Prime Factorization
Prime factorization of 84 and 105 is (2 × 2 × 3 × 7) and (3 × 5 × 7) respectively. As visible, 84 and 105 have common prime factors. Hence, the GCF of 84 and 105 is 3 × 7 = 21.
☛ Also Check:
- GCF of 50 and 60 = 10
- GCF of 24 and 80 = 8
- GCF of 210 and 90 = 30
- GCF of 50 and 80 = 10
- GCF of 54 and 32 = 2
- GCF of 80 and 20 = 20
- GCF of 24 and 60 = 12
FAQs on GCF of 84 and 105
What is the GCF of 84 and 105?
The GCF of 84 and 105 is 21. To calculate the GCF of 84 and 105, we need to factor each number (factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84; factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105) and choose the greatest factor that exactly divides both 84 and 105, i.e., 21.
How to Find the GCF of 84 and 105 by Prime Factorization?
To find the GCF of 84 and 105, we will find the prime factorization of the given numbers, i.e. 84 = 2 × 2 × 3 × 7; 105 = 3 × 5 × 7.
⇒ Since 3, 7 are common terms in the prime factorization of 84 and 105. Hence, GCF(84, 105) = 3 × 7 = 21
☛ What are Prime Numbers?
If the GCF of 105 and 84 is 21, Find its LCM.
GCF(105, 84) × LCM(105, 84) = 105 × 84
Since the GCF of 105 and 84 = 21
⇒ 21 × LCM(105, 84) = 8820
Therefore, LCM = 420
☛ GCF Calculator
What are the Methods to Find GCF of 84 and 105?
There are three commonly used methods to find the GCF of 84 and 105.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
What is the Relation Between LCM and GCF of 84, 105?
The following equation can be used to express the relation between Least Common Multiple and GCF of 84 and 105, i.e. GCF × LCM = 84 × 105.
How to Find the GCF of 84 and 105 by Long Division Method?
To find the GCF of 84, 105 using long division method, 105 is divided by 84. The corresponding divisor (21) when remainder equals 0 is taken as GCF.