HCF of 24, 48, 60 using Euclid's algorithm
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Want to know how to use Euclid’s algorithm to find the HCF of 24, 48, 60 ? Well, you have come to the right place. In this article, you will be learning about Euclid’s algorithm and how to use it to calculate the HCF with ease.
Take the help of the HCF Calculator using the Euclid Division Algorithm which finds HCF of 24, 48, 60 using Euclid's algorithm i.e 12 quickly.
Detailed Method to Find the HCF of 24,48,60 using Euclid's algorithm
Euclid’s algorithm is written as a = bq + r. This is known as the division lemma. The variable r varies according to 0 ≤ r ≤ b. We can use this to figure out the HCF of 24,48,60. This is how to do it.
Step 1: The first step is to use the division lemma with 48 and 24 because 48 is greater than 24
48 = 24 x 2 + 0
As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 24.Therefore, the HCF of 24 and 48 is equal to 24
Notice that 24 = HCF(48,24) .
Now, we must treat the HCF of the first two numbers as the next number in our calculation, and next
Step 1: The first step is to use the division lemma with 60 and 24 because 60 is greater than 24
60 = 24 x 2 + 12
Step 2: Here, the reminder 24 is not 0, we must use division lemma to 12 and 24, to get
24 = 12 x 2 + 0
As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 12.Therefore, the HCF of 24 and 60 is equal to 12
Notice that 12 = HCF(24,12) = HCF(60,24) .
Result
Hence, the HCF of 24, 48, 60 is equal to 12.
FAQ on HCF of 24, 48, 60 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid’s algorithm is represented as a = bq + r, and 0 ≤ r ≤ b..
2. How do you find HCF using Euclid's algorithm ?
Answer: Apply the division lemma to the numbers, and keep going until the remainder is zero. Once it becomes zero, the divisor will be your HCF.
3. What is the HCF of 24, 48, 60?
Answer: The HCF of 24, 48, 60 is 12.