How to find HCF of 25, 40, 45 using Euclid's Algorithm?

For arbitrary numbers 25, 40, 45 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 25, 40, 45 using Euclid's Algorithm?

For arbitrary numbers 25, 40, 45 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 25, 40, 45 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 25, 40, 45?

HCF of 25, 40, 45 is 5 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 25, 40, 45 ? 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 25, 40, 45 using Euclid's algorithm i.e 5 quickly.

Detailed Method to Find the HCF of 25,40,45 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 25,40,45. This is how to do it.

Step 1: The first step is to use the division lemma with 40 and 25 because 40 is greater than 25

40 = 25 x 1 + 15

Step 2: Here, the reminder 25 is not 0, we must use division lemma to 15 and 25, to get

25 = 15 x 1 + 10

Step 3: We consider the new divisor 15 and the new remainder 10, and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get

10 = 5 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 5.Therefore, the HCF of 25 and 40 is equal to 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) .

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 45 and 5 because 45 is greater than 5

45 = 5 x 9 + 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 5.Therefore, the HCF of 5 and 45 is equal to 5

Notice that 5 = HCF(45,5) .

Result

Hence, the HCF of 25, 40, 45 is equal to 5.

FAQ on HCF of 25, 40, 45 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 25, 40, 45?

Answer: The HCF of 25, 40, 45 is 5.