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HCF of 30 and 80

HCF of 30 and 80 is the largest possible number that divides 30 and 80 exactly without any remainder. The factors of 30 and 80 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 respectively. There are 3 commonly used methods to find the HCF of 30 and 80 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 30 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 30 and 80?

Answer: HCF of 30 and 80 is 10.

Explanation:

The HCF of two non-zero integers, x(30) and y(80), is the highest positive integer m(10) that divides both x(30) and y(80) without any remainder.

Methods to Find HCF of 30 and 80

The methods to find the HCF of 30 and 80 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

HCF of 30 and 80 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

There are 4 common factors of 30 and 80, that are 1, 2, 10, and 5. Therefore, the highest common factor of 30 and 80 is 10.

HCF of 30 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 = 30

HCF(80, 30) = HCF(30, 80 mod 30) = HCF(30, 20)
HCF(30, 20) = HCF(20, 30 mod 20) = HCF(20, 10)
HCF(20, 10) = HCF(10, 20 mod 10) = HCF(10, 0)
HCF(10, 0) = 10 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 30 and 80 is 10.

HCF of 30 and 80 by Long Division

HCF of 30 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 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the HCF of 30 and 80.

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HCF of 30 and 80 Examples

Example 1: For two numbers, HCF = 10 and LCM = 240. If one number is 30, find the other number.

Solution:

Given: HCF (x, 30) = 10 and LCM (x, 30) = 240
∵ HCF × LCM = 30 × (x)
⇒ x = (HCF × LCM)/30
⇒ x = (10 × 240)/30
⇒ x = 80
Therefore, the other number is 80.
Example 2: Find the highest number that divides 30 and 80 exactly.

Solution:

The highest number that divides 30 and 80 exactly is their highest common factor, i.e. HCF of 30 and 80.
⇒ Factors of 30 and 80:
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Therefore, the HCF of 30 and 80 is 10.
Example 3: Find the HCF of 30 and 80, if their LCM is 240.

Solution:

∵ LCM × HCF = 30 × 80
⇒ HCF(30, 80) = (30 × 80)/240 = 10
Therefore, the highest common factor of 30 and 80 is 10.

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FAQs on HCF of 30 and 80

What is the HCF of 30 and 80?

The HCF of 30 and 80 is 10. To calculate the HCF (Highest Common Factor) of 30 and 80, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the highest factor that exactly divides both 30 and 80, i.e., 10.

How to Find the HCF of 30 and 80 by Prime Factorization?

To find the HCF of 30 and 80, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 80 = 2 × 2 × 2 × 2 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 30 and 80. Hence, HCF(30, 80) = 2 × 5 = 10
☛ What are Prime Numbers?

How to Find the HCF of 30 and 80 by Long Division Method?

To find the HCF of 30, 80 using long division method, 80 is divided by 30. The corresponding divisor (10) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 30, 80?

The following equation can be used to express the relation between LCM and HCF of 30 and 80, i.e. HCF × LCM = 30 × 80.

If the HCF of 80 and 30 is 10, Find its LCM.

HCF(80, 30) × LCM(80, 30) = 80 × 30
Since the HCF of 80 and 30 = 10
⇒ 10 × LCM(80, 30) = 2400
Therefore, LCM = 240
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What are the Methods to Find HCF of 30 and 80?

There are three commonly used methods to find the HCF of 30 and 80.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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