HCF of 324 and 144

HCF of 324 and 144 is the largest possible number that divides 324 and 144 exactly without any remainder. The factors of 324 and 144 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 respectively. There are 3 commonly used methods to find the HCF of 324 and 144 - prime factorization, Euclidean algorithm, and long division.

Answer: HCF of 324 and 144 is 36.

Explanation:

The HCF of two non-zero integers, x(324) and y(144), is the highest positive integer m(36) that divides both x(324) and y(144) without any remainder.

The methods to find the HCF of 324 and 144 are explained below.

• Listing Common Factors
• Long Division Method
• Using Euclid's Algorithm

HCF of 324 and 144 by Listing Common Factors

• Factors of 324: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
• Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

There are 9 common factors of 324 and 144, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the highest common factor of 324 and 144 is 36.

HCF of 324 and 144 by Long Division

HCF of 324 and 144 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 324 (larger number) by 144 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (144) by the remainder (36).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (36) is the HCF of 324 and 144.

HCF of 324 and 144 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 = 324 and Y = 144

• HCF(324, 144) = HCF(144, 324 mod 144) = HCF(144, 36)
• HCF(144, 36) = HCF(36, 144 mod 36) = HCF(36, 0)
• HCF(36, 0) = 36 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 324 and 144 is 36.

☛ Also Check:

• HCF of 18 and 20 = 2
• HCF of 6, 8 and 12 = 2
• HCF of 867 and 225 = 3
• HCF of 1650 and 847 = 11
• HCF of 81 and 237 = 3
• HCF of 100 and 190 = 10
• HCF of 36, 42 and 48 = 6

FAQs on HCF of 324 and 144

What is the HCF of 324 and 144?

The HCF of 324 and 144 is 36. To calculate the Highest common factor of 324 and 144, we need to factor each number (factors of 324 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324; factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144) and choose the highest factor that exactly divides both 324 and 144, i.e., 36.

How to Find the HCF of 324 and 144 by Prime Factorization?

To find the HCF of 324 and 144, we will find the prime factorization of the given numbers, i.e. 324 = 2 × 2 × 3 × 3 × 3 × 3; 144 = 2 × 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 324 and 144. Hence, HCF(324, 144) = 2 × 2 × 3 × 3 = 36
☛ What are Prime Numbers?

If the HCF of 144 and 324 is 36, Find its LCM.

HCF(144, 324) × LCM(144, 324) = 144 × 324
Since the HCF of 144 and 324 = 36
⇒ 36 × LCM(144, 324) = 46656
Therefore, LCM = 1296
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 324 and 144?

There are three commonly used methods to find the HCF of 324 and 144.

• By Euclidean Algorithm
• By Prime Factorization
• By Long Division

What is the Relation Between LCM and HCF of 324, 144?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 324 and 144, i.e. HCF × LCM = 324 × 144.

How to Find the HCF of 324 and 144 by Long Division Method?

To find the HCF of 324, 144 using long division method, 324 is divided by 144. The corresponding divisor (36) when remainder equals 0 is taken as HCF.