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HCF of 32 and 40

HCF of 32 and 40 is the largest possible number that divides 32 and 40 exactly without any remainder. The factors of 32 and 40 are 1, 2, 4, 8, 16, 32 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the HCF of 32 and 40 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 32 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 32 and 40?

Answer: HCF of 32 and 40 is 8.

Explanation:

The HCF of two non-zero integers, x(32) and y(40), is the highest positive integer m(8) that divides both x(32) and y(40) without any remainder.

Methods to Find HCF of 32 and 40

The methods to find the HCF of 32 and 40 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

HCF of 32 and 40 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 = 40 and Y = 32

HCF(40, 32) = HCF(32, 40 mod 32) = HCF(32, 8)
HCF(32, 8) = HCF(8, 32 mod 8) = HCF(8, 0)
HCF(8, 0) = 8 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 32 and 40 is 8.

HCF of 32 and 40 by Long Division

HCF of 32 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the HCF of 32 and 40.

HCF of 32 and 40 by Listing Common Factors

Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 4 common factors of 32 and 40, that are 8, 1, 2, and 4. Therefore, the highest common factor of 32 and 40 is 8.

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HCF of 32 and 40 Examples

Example 1: Find the HCF of 32 and 40, if their LCM is 160.

Solution:

∵ LCM × HCF = 32 × 40
⇒ HCF(32, 40) = (32 × 40)/160 = 8
Therefore, the highest common factor of 32 and 40 is 8.
Example 2: Find the highest number that divides 32 and 40 exactly.

Solution:

The highest number that divides 32 and 40 exactly is their highest common factor, i.e. HCF of 32 and 40.
⇒ Factors of 32 and 40:
- Factors of 32 = 1, 2, 4, 8, 16, 32
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Therefore, the HCF of 32 and 40 is 8.
Example 3: For two numbers, HCF = 8 and LCM = 160. If one number is 32, find the other number.

Solution:

Given: HCF (y, 32) = 8 and LCM (y, 32) = 160
∵ HCF × LCM = 32 × (y)
⇒ y = (HCF × LCM)/32
⇒ y = (8 × 160)/32
⇒ y = 40
Therefore, the other number is 40.

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FAQs on HCF of 32 and 40

What is the HCF of 32 and 40?

The HCF of 32 and 40 is 8. To calculate the Highest common factor (HCF) of 32 and 40, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the highest factor that exactly divides both 32 and 40, i.e., 8.

If the HCF of 40 and 32 is 8, Find its LCM.

HCF(40, 32) × LCM(40, 32) = 40 × 32
Since the HCF of 40 and 32 = 8
⇒ 8 × LCM(40, 32) = 1280
Therefore, LCM = 160
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How to Find the HCF of 32 and 40 by Long Division Method?

To find the HCF of 32, 40 using long division method, 40 is divided by 32. The corresponding divisor (8) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 32, 40?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 32 and 40, i.e. HCF × LCM = 32 × 40.

How to Find the HCF of 32 and 40 by Prime Factorization?

To find the HCF of 32 and 40, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 32 and 40. Hence, HCF(32, 40) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

What are the Methods to Find HCF of 32 and 40?

There are three commonly used methods to find the HCF of 32 and 40.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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