HCF of 30 and 42

The HCF of 30 and 42 is 6. The highest possible number that divides 30 and 42 perfectly without any residue is the HCF of 30 and 42. 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 3, 6, 7, 14, 21, 42 are the factors of 30 and 42, respectively. Prime factorisation, the listing common factors, and long division are three common methods for calculating the HCF of 30 and 42.

Also read: Highest common factor

What is the HCF of 30 and 42?

The answer to this question is 6. This article shows the HCF of 30 and 42 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 30 and 42?

There are three methods to find the HCF of 30 and 42:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 30 and 42 by Prime Factorisation Method

The prime factorisation of 30 and 42 is given by:

Prime factorisation of 30 = (2 × 3 × 5)

Prime factorisation of 42 = (2 × 3 × 7)

Hence, the HCF of 30 and 42 is 2 × 3 = 6.

HCF (30, 42) = 6

HCF of 30 and 42 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 30 and 42.

HCF of 30 and 42

No further division can be done.

Hence, HCF (30, 42) = 6

HCF of 30 and 42 by Listing the Factors

To calculate the HCF of 30 and 42 by listing out the common factors, list the factors as shown below:

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; they are 1, 2, 3, and 6. Therefore, the highest common factor of 30 and 42 is 6.

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Video Lesson on Properties of HCF and LCM

HCF of 30 and 42 Solved Example

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.

Frequently Asked Questions on HCF of 30 and 42

Q1

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.
Q2

How to find the HCF of 30 and 42 by prime factorisation?

To find the HCF of 30 and 42, we will find the prime factorisation of the given numbers, i.e. 30 = 2 × 3 × 5; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common numbers in the prime factorisation of 30 and 42, HCF(30, 42) = 2 × 3 = 6
Q3

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 Listing Common Factors
By Prime Factorisation

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