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.
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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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
What is the HCF of 30 and 42?
How to find the HCF of 30 and 42 by prime factorisation?
⇒ Since 2, 3 are common numbers in the prime factorisation of 30 and 42, HCF(30, 42) = 2 × 3 = 6
What are the methods to find HCF of 30 and 42?
By Long Division
By Listing Common Factors
By Prime Factorisation
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