HCF of 144 and 192
HCF of 144 and 192 is the largest possible number that divides 144 and 192 exactly without any remainder. The factors of 144 and 192 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192 respectively. There are 3 commonly used methods to find the HCF of 144 and 192 - Euclidean algorithm, prime factorization, and long division.
| 1. | HCF of 144 and 192 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 144 and 192?
Answer: HCF of 144 and 192 is 48.
Explanation:
The HCF of two non-zero integers, x(144) and y(192), is the highest positive integer m(48) that divides both x(144) and y(192) without any remainder.
Methods to Find HCF of 144 and 192
Let's look at the different methods for finding the HCF of 144 and 192.
- Prime Factorization Method
- Listing Common Factors
- Long Division Method
HCF of 144 and 192 by Prime Factorization
Prime factorization of 144 and 192 is (2 × 2 × 2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 2 × 2 × 3) respectively. As visible, 144 and 192 have common prime factors. Hence, the HCF of 144 and 192 is 2 × 2 × 2 × 2 × 3 = 48.
HCF of 144 and 192 by Listing Common Factors
- Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
- Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
There are 10 common factors of 144 and 192, that are 1, 2, 3, 4, 6, 8, 12, 16, 48, and 24. Therefore, the highest common factor of 144 and 192 is 48.
HCF of 144 and 192 by Long Division
HCF of 144 and 192 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 192 (larger number) by 144 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (144) by the remainder (48).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (48) is the HCF of 144 and 192.
☛ Also Check:
- HCF of 84 and 120 = 12
- HCF of 1 and 2 = 1
- HCF of 12, 16 and 24 = 4
- HCF of 84 and 90 = 6
- HCF of 2, 3 and 4 = 1
- HCF of 20, 25 and 30 = 5
- HCF of 825, 675 and 450 = 75
FAQs on HCF of 144 and 192
What is the HCF of 144 and 192?
The HCF of 144 and 192 is 48. To calculate the Highest common factor (HCF) of 144 and 192, we need to factor each number (factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144; factors of 192 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192) and choose the highest factor that exactly divides both 144 and 192, i.e., 48.
If the HCF of 192 and 144 is 48, Find its LCM.
HCF(192, 144) × LCM(192, 144) = 192 × 144
Since the HCF of 192 and 144 = 48
⇒ 48 × LCM(192, 144) = 27648
Therefore, LCM = 576
☛ HCF Calculator
How to Find the HCF of 144 and 192 by Prime Factorization?
To find the HCF of 144 and 192, we will find the prime factorization of the given numbers, i.e. 144 = 2 × 2 × 2 × 2 × 3 × 3; 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 2, 3 are common terms in the prime factorization of 144 and 192. Hence, HCF(144, 192) = 2 × 2 × 2 × 2 × 3 = 48
☛ What are Prime Numbers?
What are the Methods to Find HCF of 144 and 192?
There are three commonly used methods to find the HCF of 144 and 192.
- By Long Division
- By Prime Factorization
- By Listing Common Factors
How to Find the HCF of 144 and 192 by Long Division Method?
To find the HCF of 144, 192 using long division method, 192 is divided by 144. The corresponding divisor (48) when remainder equals 0 is taken as HCF.
What is the Relation Between LCM and HCF of 144, 192?
The following equation can be used to express the relation between LCM and HCF of 144 and 192, i.e. HCF × LCM = 144 × 192.