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HCF of 144 and 198

HCF of 144 and 198 is the largest possible number that divides 144 and 198 exactly without any remainder. The factors of 144 and 198 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 and 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198 respectively. There are 3 commonly used methods to find the HCF of 144 and 198 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 144 and 198
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 144 and 198?

Answer: HCF of 144 and 198 is 18.

Explanation:

The HCF of two non-zero integers, x(144) and y(198), is the highest positive integer m(18) that divides both x(144) and y(198) without any remainder.

Methods to Find HCF of 144 and 198

The methods to find the HCF of 144 and 198 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 144 and 198 by Prime Factorization

Prime factorization of 144 and 198 is (2 × 2 × 2 × 2 × 3 × 3) and (2 × 3 × 3 × 11) respectively. As visible, 144 and 198 have common prime factors. Hence, the HCF of 144 and 198 is 2 × 3 × 3 = 18.

HCF of 144 and 198 by Long Division

HCF of 144 and 198 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 198 (larger number) by 144 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (144) by the remainder (54).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (18) is the HCF of 144 and 198.

HCF of 144 and 198 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 198 and Y = 144

HCF(198, 144) = HCF(144, 198 mod 144) = HCF(144, 54)
HCF(144, 54) = HCF(54, 144 mod 54) = HCF(54, 36)
HCF(54, 36) = HCF(36, 54 mod 36) = HCF(36, 18)
HCF(36, 18) = HCF(18, 36 mod 18) = HCF(18, 0)
HCF(18, 0) = 18 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 144 and 198 is 18.

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HCF of 144 and 198 Examples

Example 1: Find the HCF of 144 and 198, if their LCM is 1584.

Solution:

∵ LCM × HCF = 144 × 198
⇒ HCF(144, 198) = (144 × 198)/1584 = 18
Therefore, the highest common factor of 144 and 198 is 18.
Example 2: Find the highest number that divides 144 and 198 exactly.

Solution:

The highest number that divides 144 and 198 exactly is their highest common factor, i.e. HCF of 144 and 198.
⇒ Factors of 144 and 198:
- Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
- Factors of 198 = 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
Therefore, the HCF of 144 and 198 is 18.
Example 3: For two numbers, HCF = 18 and LCM = 1584. If one number is 144, find the other number.

Solution:

Given: HCF (z, 144) = 18 and LCM (z, 144) = 1584
∵ HCF × LCM = 144 × (z)
⇒ z = (HCF × LCM)/144
⇒ z = (18 × 1584)/144
⇒ z = 198
Therefore, the other number is 198.

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FAQs on HCF of 144 and 198

What is the HCF of 144 and 198?

The HCF of 144 and 198 is 18. To calculate the Highest common factor of 144 and 198, 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 198 = 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198) and choose the highest factor that exactly divides both 144 and 198, i.e., 18.

If the HCF of 198 and 144 is 18, Find its LCM.

HCF(198, 144) × LCM(198, 144) = 198 × 144
Since the HCF of 198 and 144 = 18
⇒ 18 × LCM(198, 144) = 28512
Therefore, LCM = 1584
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How to Find the HCF of 144 and 198 by Long Division Method?

To find the HCF of 144, 198 using long division method, 198 is divided by 144. The corresponding divisor (18) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 144, 198?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 144 and 198, i.e. HCF × LCM = 144 × 198.

What are the Methods to Find HCF of 144 and 198?

There are three commonly used methods to find the HCF of 144 and 198.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the HCF of 144 and 198 by Prime Factorization?

To find the HCF of 144 and 198, we will find the prime factorization of the given numbers, i.e. 144 = 2 × 2 × 2 × 2 × 3 × 3; 198 = 2 × 3 × 3 × 11.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 144 and 198. Hence, HCF(144, 198) = 2 × 3 × 3 = 18
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