The HCF of 144 and 192 is 48. The greatest number that divides 144 and 192 exactly and without a remainder is the HCF of these numbers. The factors of 144 and 192 are:
144 → 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
192 → 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
The listing common factors, prime factorisation and long division are the three most frequent methods for calculating the HCF of 144 and 192.
Also read: Highest common factor
What is the HCF of 144 and 192?
The answer to this question is 48. This article shows the HCF of 144 and 192 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.
How to Find HCF of 144 and 192?
There are three methods to find the HCF of 144 and 192:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 144 and 192 by Prime Factorisation Method
The prime factorisation of 144 and 192 is given by:
Prime factorisation of 144 = (2 × 2 × 2 × 2 × 3 × 3)
Prime factorisation of 192 = (2 × 2 × 2 × 2 × 2 × 2 × 3)
Hence, the HCF of 144 and 192 is 2 × 2 × 2 × 2 × 3 = 48
HCF (144, 192) = 48
HCF of 144 and 192 by Long Division Method
The divisor that we get when the remainder is 0 after doing long division repeatedly is the HCF of 144 and 192.
No further division can be done.
Hence, HCF (144, 192) = 48
HCF of 144 and 192 by Listing Common Factors
To calculate the HCF of 144 and 192 by listing common factors, list the factors as shown below:
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, and they are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Therefore, the Highest Common Factor of 144 and 192 is 48.
Related Articles
Video Lesson on Properties of HCF and LCM
HCF of 144 and 192 Solved Example
The product of two numbers is 27648. If their HCF is 48, what is their LCM?
Solution:
Given: HCF = 48 and product of numbers = 27648
We have LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 27648/48
Therefore, the LCM is 576.
Frequently Asked Questions on HCF of 144 and 192
What is the HCF of 144 and 192?
How to find the HCF of 144 and 192 by prime factorisation?
⇒ 2, 2, 2, 2, 3 are common terms in the prime factorisation of 144 and 192. Hence, HCF(144, 192) = 2 × 2 × 2 × 2 × 3 = 48
What are the methods to find HCF of 144 and 192?
Long Division
Listing Common Factors
Prime Factorisation
If the HCF of 192 and 144 is 48, find its LCM.
The HCF of 192 and 144 = 48
⇒ 48 × LCM(192, 144) = 27648
Therefore, LCM = 576
Comments