How to find HCF of 36, 45, 60 using Euclid's Algorithm?

For arbitrary numbers 36, 45, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.

How to find HCF of 36, 45, 60 using Euclid's Algorithm?

For arbitrary numbers 36, 45, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.

HCF of 36, 45, 60 using Euclid's algorithm

Q: What is the Euclid division algorithm?

Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

Q: what is the HCF of 36, 45, 60?

HCF of 36, 45, 60 is 3 the largest number that divides all the numbers leaving a remainder zero.

Created By : Jatin Gogia
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023

Want to know how to use Euclid’s algorithm to find the HCF of 36, 45, 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 36, 45, 60 using Euclid's algorithm i.e 3 quickly.

Detailed Method to Find the HCF of 36,45,60 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 36,45,60. This is how to do it.

Step 1: The first step is to use the division lemma with 45 and 36 because 45 is greater than 36

45 = 36 x 1 + 9

Step 2: Here, the reminder 36 is not 0, we must use division lemma to 9 and 36, to get

36 = 9 x 4 + 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 9.Therefore, the HCF of 36 and 45 is equal to 9

Notice that 9 = HCF(36,9) = HCF(45,36) .

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 9 because 60 is greater than 9

60 = 9 x 6 + 6

Step 2: Here, the reminder 9 is not 0, we must use division lemma to 6 and 9, to get

9 = 6 x 1 + 3

Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get

6 = 3 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 3.Therefore, the HCF of 9 and 60 is equal to 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) .

Result

Hence, the HCF of 36, 45, 60 is equal to 3.

FAQ on HCF of 36, 45, 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 36, 45, 60?

Answer: The HCF of 36, 45, 60 is 3.