HCF of 45, 75, 90, 123 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 45, 75, 90, 123 ? 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 45, 75, 90, 123 using Euclid's algorithm i.e 3 quickly.
Detailed Method to Find the HCF of 45,75,90,123 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 45,75,90,123. This is how to do it.
Step 1: The first step is to use the division lemma with 75 and 45 because 75 is greater than 45
75 = 45 x 1 + 30
Step 2: Here, the reminder 45 is not 0, we must use division lemma to 30 and 45, to get
45 = 30 x 1 + 15
Step 3: We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get
30 = 15 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 15.Therefore, the HCF of 45 and 75 is equal to 15
Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(75,45) .
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 90 and 15 because 90 is greater than 15
90 = 15 x 6 + 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 15.Therefore, the HCF of 15 and 90 is equal to 15
Notice that 15 = HCF(90,15) .
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 123 and 15 because 123 is greater than 15
123 = 15 x 8 + 3
Step 2: Here, the reminder 15 is not 0, we must use division lemma to 3 and 15, to get
15 = 3 x 5 + 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 15 and 123 is equal to 3
Notice that 3 = HCF(15,3) = HCF(123,15) .
Result
Hence, the HCF of 45, 75, 90, 123 is equal to 3.
FAQ on HCF of 45, 75, 90, 123 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 45, 75, 90, 123?
Answer: The HCF of 45, 75, 90, 123 is 3.