The HCF of 20 and 30 is 10. The greatest possible number that divides 20 and 30 perfectly without any remainder is the HCF of 20 and 30. The factors of 20 and 30 are 1, 2, 4, 5, 10, 20 and 1, 2, 3, 5, 6, 10, 15, 30, respectively. Prime factorisation, listing common factors, and long division are three frequently used methods for calculating the HCF of 20 and 30.
Also read: Highest common factor
What is HCF of 20 and 30?
The answer to this question is 10. This article shows how to find the HCF of 20 and 30 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 20 and 30?
There are three methods to find the HCF of 20 and 30:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 20 and 30 by Prime Factorisation Method
The prime factorisation of 20 and 30 is given by:
Prime factorisation of 20 = (2 × 2 × 5)
Prime factorisation of 30 = (2 × 3 × 5)
The common prime factors of 20 and 30 are 2 and 5.
Hence, HCF (20, 30) = 2 × 5 = 10
HCF of 20 and 30 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 20 and 30.
No further division can be done.
Hence, HCF (20, 30) = 10
HCF of 20 and 30 by Listing Common Factors
To calculate the HCF of 20 and 30 by listing out the common factors, list the factors as shown below:
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
There are 4 common factors of 20 and 30; they are 1, 2, 5, and 10.
Therefore, the highest common factor of 20 and 30 is 10.
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Video Lesson on Properties of HCF and LCM
HCF of 20 and 30 Solved Example
Question: For two numbers, HCF = 10 and LCM = 60. If one number is 30, find the other number.
Solution:
Given: HCF (x, 30) = 10 and LCM (x, 30) = 60
∵ HCF × LCM = 30 × (x)
⇒ x = (HCF × LCM)/30
⇒ x = (10 × 60)/30
⇒ x = 20
Therefore, the other number is 20.
Frequently Asked Questions on HCF of 20 and 30
Q1
What is the HCF of 20 and 30?
The HCF of 20 and 30 is 10. To calculate the highest common factor (HCF) of 20 and 30, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the highest factor that exactly divides both 20 and 30, i.e. 10.
Q2
How to find the HCF of 20 and 30 by Prime Factorisation?
To find the HCF of 20 and 30, we will find the prime factorisation of the given numbers, i.e. 20 = 2 × 2 × 5; 30 = 2 × 3 × 5. ⇒ 2 and 5 are common numbers in the prime factorisation of 20 and 30. Hence, HCF(20, 30) = 2 × 5 = 10
Q3
How to Find the HCF of 20 and 30 by Long Division Method?
To find the HCF of 20, 30 using the long division method, 30 is divided by 20. The corresponding divisor (10) when remainder equals 0 is taken as HCF.
