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HCF of 64 and 72

HCF of 64 and 72 is the largest possible number that divides 64 and 72 exactly without any remainder. The factors of 64 and 72 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the HCF of 64 and 72 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 64 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 64 and 72?

Answer: HCF of 64 and 72 is 8.

Explanation:

The HCF of two non-zero integers, x(64) and y(72), is the highest positive integer m(8) that divides both x(64) and y(72) without any remainder.

Methods to Find HCF of 64 and 72

The methods to find the HCF of 64 and 72 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Prime Factorization Method

HCF of 64 and 72 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 = 72 and Y = 64

HCF(72, 64) = HCF(64, 72 mod 64) = HCF(64, 8)
HCF(64, 8) = HCF(8, 64 mod 8) = HCF(8, 0)
HCF(8, 0) = 8 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 64 and 72 is 8.

HCF of 64 and 72 by Listing Common Factors

Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

There are 4 common factors of 64 and 72, that are 8, 1, 2, and 4. Therefore, the highest common factor of 64 and 72 is 8.

HCF of 64 and 72 by Prime Factorization

Prime factorization of 64 and 72 is (2 × 2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 64 and 72 have common prime factors. Hence, the HCF of 64 and 72 is 2 × 2 × 2 = 8.

☛ Also Check:

HCF of 64 and 72 Examples

Example 1: Find the HCF of 64 and 72, if their LCM is 576.

Solution:

∵ LCM × HCF = 64 × 72
⇒ HCF(64, 72) = (64 × 72)/576 = 8
Therefore, the highest common factor of 64 and 72 is 8.
Example 2: For two numbers, HCF = 8 and LCM = 576. If one number is 72, find the other number.

Solution:

Given: HCF (x, 72) = 8 and LCM (x, 72) = 576
∵ HCF × LCM = 72 × (x)
⇒ x = (HCF × LCM)/72
⇒ x = (8 × 576)/72
⇒ x = 64
Therefore, the other number is 64.
Example 3: Find the highest number that divides 64 and 72 exactly.

Solution:

The highest number that divides 64 and 72 exactly is their highest common factor, i.e. HCF of 64 and 72.
⇒ Factors of 64 and 72:
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the HCF of 64 and 72 is 8.

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FAQs on HCF of 64 and 72

What is the HCF of 64 and 72?

The HCF of 64 and 72 is 8. To calculate the HCF of 64 and 72, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the highest factor that exactly divides both 64 and 72, i.e., 8.

What is the Relation Between LCM and HCF of 64, 72?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 64 and 72, i.e. HCF × LCM = 64 × 72.

How to Find the HCF of 64 and 72 by Long Division Method?

To find the HCF of 64, 72 using long division method, 72 is divided by 64. The corresponding divisor (8) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 64 and 72?

There are three commonly used methods to find the HCF of 64 and 72.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the HCF of 64 and 72 by Prime Factorization?

To find the HCF of 64 and 72, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 64 and 72. Hence, HCF(64, 72) = 2 × 2 × 2 = 8
☛ What are Prime Numbers?

If the HCF of 72 and 64 is 8, Find its LCM.

HCF(72, 64) × LCM(72, 64) = 72 × 64
Since the HCF of 72 and 64 = 8
⇒ 8 × LCM(72, 64) = 4608
Therefore, LCM = 576
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