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HCF of 30 and 42

HCF of 30 and 42 is the largest possible number that divides 30 and 42 exactly without any remainder. The factors of 30 and 42 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the HCF of 30 and 42 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 30 and 42
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 30 and 42?

Answer: HCF of 30 and 42 is 6.

Explanation:

The HCF of two non-zero integers, x(30) and y(42), is the highest positive integer m(6) that divides both x(30) and y(42) without any remainder.

Methods to Find HCF of 30 and 42

The methods to find the HCF of 30 and 42 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

HCF of 30 and 42 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 = 42 and Y = 30

HCF(42, 30) = HCF(30, 42 mod 30) = HCF(30, 12)
HCF(30, 12) = HCF(12, 30 mod 12) = HCF(12, 6)
HCF(12, 6) = HCF(6, 12 mod 6) = HCF(6, 0)
HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 30 and 42 is 6.

HCF of 30 and 42 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

There are 4 common factors of 30 and 42, that are 1, 2, 3, and 6. Therefore, the highest common factor of 30 and 42 is 6.

HCF of 30 and 42 by Long Division

HCF of 30 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 42 (larger number) by 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 30 and 42.

☛ Also Check:

HCF of 30 and 42 Examples

Example 1: For two numbers, HCF = 6 and LCM = 210. If one number is 30, find the other number.

Solution:

Given: HCF (y, 30) = 6 and LCM (y, 30) = 210
∵ HCF × LCM = 30 × (y)
⇒ y = (HCF × LCM)/30
⇒ y = (6 × 210)/30
⇒ y = 42
Therefore, the other number is 42.
Example 2: Find the HCF of 30 and 42, if their LCM is 210.

Solution:

∵ LCM × HCF = 30 × 42
⇒ HCF(30, 42) = (30 × 42)/210 = 6
Therefore, the highest common factor of 30 and 42 is 6.
Example 3: The product of two numbers is 1260. If their HCF is 6, what is their LCM?

Solution:

Given: HCF = 6 and product of numbers = 1260
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1260/6
Therefore, the LCM is 210.

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FAQs on HCF of 30 and 42

What is the HCF of 30 and 42?

The HCF of 30 and 42 is 6. To calculate the HCF of 30 and 42, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the highest factor that exactly divides both 30 and 42, i.e., 6.

How to Find the HCF of 30 and 42 by Prime Factorization?

To find the HCF of 30 and 42, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 30 and 42. Hence, HCF(30, 42) = 2 × 3 = 6
☛ What are Prime Numbers?

If the HCF of 42 and 30 is 6, Find its LCM.

HCF(42, 30) × LCM(42, 30) = 42 × 30
Since the HCF of 42 and 30 = 6
⇒ 6 × LCM(42, 30) = 1260
Therefore, LCM = 210
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 30 and 42?

There are three commonly used methods to find the HCF of 30 and 42.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and HCF of 30, 42?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 30 and 42, i.e. HCF × LCM = 30 × 42.

How to Find the HCF of 30 and 42 by Long Division Method?

To find the HCF of 30, 42 using long division method, 42 is divided by 30. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

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