GCF of 120 and 168
GCF of 120 and 168 is the largest possible number that divides 120 and 168 exactly without any remainder. The factors of 120 and 168 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 respectively. There are 3 commonly used methods to find the GCF of 120 and 168 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 120 and 168 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 120 and 168?
Answer: GCF of 120 and 168 is 24.
Explanation:
The GCF of two non-zero integers, x(120) and y(168), is the greatest positive integer m(24) that divides both x(120) and y(168) without any remainder.
Methods to Find GCF of 120 and 168
The methods to find the GCF of 120 and 168 are explained below.
- Long Division Method
- Prime Factorization Method
- Listing Common Factors
GCF of 120 and 168 by Long Division
GCF of 120 and 168 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 168 (larger number) by 120 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (120) by the remainder (48).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (24) is the GCF of 120 and 168.
GCF of 120 and 168 by Prime Factorization
Prime factorization of 120 and 168 is (2 × 2 × 2 × 3 × 5) and (2 × 2 × 2 × 3 × 7) respectively. As visible, 120 and 168 have common prime factors. Hence, the GCF of 120 and 168 is 2 × 2 × 2 × 3 = 24.
GCF of 120 and 168 by Listing Common Factors
- Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
- Factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
There are 8 common factors of 120 and 168, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest common factor of 120 and 168 is 24.
☛ Also Check:
- GCF of 52 and 65 = 13
- GCF of 12 and 13 = 1
- GCF of 12 and 36 = 12
- GCF of 10 and 16 = 2
- GCF of 54 and 72 = 18
- GCF of 6 and 14 = 2
- GCF of 12 and 14 = 2
FAQs on GCF of 120 and 168
What is the GCF of 120 and 168?
The GCF of 120 and 168 is 24. To calculate the greatest common factor (GCF) of 120 and 168, we need to factor each number (factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120; factors of 168 = 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168) and choose the greatest factor that exactly divides both 120 and 168, i.e., 24.
If the GCF of 168 and 120 is 24, Find its LCM.
GCF(168, 120) × LCM(168, 120) = 168 × 120
Since the GCF of 168 and 120 = 24
⇒ 24 × LCM(168, 120) = 20160
Therefore, LCM = 840
☛ Greatest Common Factor Calculator
What are the Methods to Find GCF of 120 and 168?
There are three commonly used methods to find the GCF of 120 and 168.
- By Euclidean Algorithm
- By Prime Factorization
- By Long Division
How to Find the GCF of 120 and 168 by Prime Factorization?
To find the GCF of 120 and 168, we will find the prime factorization of the given numbers, i.e. 120 = 2 × 2 × 2 × 3 × 5; 168 = 2 × 2 × 2 × 3 × 7.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 120 and 168. Hence, GCF(120, 168) = 2 × 2 × 2 × 3 = 24
☛ What is a Prime Number?
What is the Relation Between LCM and GCF of 120, 168?
The following equation can be used to express the relation between LCM and GCF of 120 and 168, i.e. GCF × LCM = 120 × 168.
How to Find the GCF of 120 and 168 by Long Division Method?
To find the GCF of 120, 168 using long division method, 168 is divided by 120. The corresponding divisor (24) when remainder equals 0 is taken as GCF.