The HCF of 18 and 42 is 6. The greatest number that divides 18 and 42 perfectly without leaving a remainder is the HCF of 18 and 42. The factors of 18 and 42 are 1, 2, 3, 6, 9, and, 1, 2, 3, 6, 7, 14, 42, respectively. Listing common factors, prime factorisation, and long division are the three most frequent methods used for calculating the HCF of 18 and 42.
Also read: Highest common factor
What is the HCF of 18 and 42?
The answer to this question is 6. This article shows how to find the HCF of 18 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 18 and 42?
There are three methods to find the HCF of 18 and 42:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 18 and 42 by Prime Factorisation Method
The prime factorisation of 18 and 42 is given by:
Prime factorisation of 18 = (2 × 3 × 3)
Prime factorisation of 42 = (2 × 3 × 7)
Hence, the HCF of 18 and 42 is 2 × 3 = 6.
HCF (18, 42) = 6
HCF of 18 and 42 by Long Division Method
The divisor we receive when the remainder is 0 after repeatedly doing a long division is the HCF of 18 and 42.
No further division can be done.
Hence, HCF (18, 42) = 6
HCF of 18 and 42 by Listing Common Factors
To calculate the HCF of 18 and 42 by listing out the common factors, list the factors as shown below:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 18 and 42, and they are 1, 2, 3, and 6. Therefore, the Highest Common Factor of 18 and 42 is 6.
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Video Lesson on Properties of HCF and LCM
HCF of 18 and 42 Solved Example
The product of two numbers is 756. If their HCF is 6, what is their LCM?
Solution:
Given: HCF = 6 and product of numbers = 756
We know that LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 756/6
Therefore, the LCM is 126.
Frequently Asked Questions on HCF of 18 and 42
What is the HCF of 18 and 42?
How to find the HCF of 18 and 42 by prime factorisation?
⇒ 2, 3 are the common factors in the prime factorisation of 18 and 42. Hence, HCF (18, 42) = 2 × 3 = 6
What are the methods to find HCF of 18 and 42?
Long Division
Listing Common Factors
Prime Factorisation
If the HCF of 42 and 18 is 6, find its LCM.
The HCF of 42 and 18 = 6
⇒ 6 × LCM(42, 18) = 756
Therefore, LCM = 126
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