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HCF of 40 and 80

HCF of 40 and 80 is the largest possible number that divides 40 and 80 exactly without any remainder. The factors of 40 and 80 are 1, 2, 4, 5, 8, 10, 20, 40 and 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 respectively. There are 3 commonly used methods to find the HCF of 40 and 80 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 40 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 40 and 80?

Answer: HCF of 40 and 80 is 40.

Explanation:

The HCF of two non-zero integers, x(40) and y(80), is the highest positive integer m(40) that divides both x(40) and y(80) without any remainder.

Methods to Find HCF of 40 and 80

The methods to find the HCF of 40 and 80 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 40 and 80 by Prime Factorization

Prime factorization of 40 and 80 is (2 × 2 × 2 × 5) and (2 × 2 × 2 × 2 × 5) respectively. As visible, 40 and 80 have common prime factors. Hence, the HCF of 40 and 80 is 2 × 2 × 2 × 5 = 40.

HCF of 40 and 80 by Long Division

HCF of 40 and 80 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 80 (larger number) by 40 (smaller number).
Step 2: Since the remainder = 0, the divisor (40) is the HCF of 40 and 80.

The corresponding divisor (40) is the HCF of 40 and 80.

HCF of 40 and 80 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 = 80 and Y = 40

HCF(80, 40) = HCF(40, 80 mod 40) = HCF(40, 0)
HCF(40, 0) = 40 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 40 and 80 is 40.

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HCF of 40 and 80 Examples

Example 1: The product of two numbers is 3200. If their HCF is 40, what is their LCM?

Solution:

Given: HCF = 40 and product of numbers = 3200
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 3200/40
Therefore, the LCM is 80.
Example 2: Find the HCF of 40 and 80, if their LCM is 80.

Solution:

∵ LCM × HCF = 40 × 80
⇒ HCF(40, 80) = (40 × 80)/80 = 40
Therefore, the highest common factor of 40 and 80 is 40.
Example 3: For two numbers, HCF = 40 and LCM = 80. If one number is 40, find the other number.

Solution:

Given: HCF (z, 40) = 40 and LCM (z, 40) = 80
∵ HCF × LCM = 40 × (z)
⇒ z = (HCF × LCM)/40
⇒ z = (40 × 80)/40
⇒ z = 80
Therefore, the other number is 80.

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FAQs on HCF of 40 and 80

What is the HCF of 40 and 80?

The HCF of 40 and 80 is 40. To calculate the HCF (Highest Common Factor) of 40 and 80, we need to factor each number (factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the highest factor that exactly divides both 40 and 80, i.e., 40.

How to Find the HCF of 40 and 80 by Prime Factorization?

To find the HCF of 40 and 80, we will find the prime factorization of the given numbers, i.e. 40 = 2 × 2 × 2 × 5; 80 = 2 × 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2, 5 are common terms in the prime factorization of 40 and 80. Hence, HCF(40, 80) = 2 × 2 × 2 × 5 = 40
☛ Prime Number

What is the Relation Between LCM and HCF of 40, 80?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 40 and 80, i.e. HCF × LCM = 40 × 80.

What are the Methods to Find HCF of 40 and 80?

There are three commonly used methods to find the HCF of 40 and 80.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the HCF of 40 and 80 by Long Division Method?

To find the HCF of 40, 80 using long division method, 80 is divided by 40. The corresponding divisor (40) when remainder equals 0 is taken as HCF.

If the HCF of 80 and 40 is 40, Find its LCM.

HCF(80, 40) × LCM(80, 40) = 80 × 40
Since the HCF of 80 and 40 = 40
⇒ 40 × LCM(80, 40) = 3200
Therefore, LCM = 80
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