Highest Common Factor of 198, 2021 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 198, 2021 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 198, 2021 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 198, 2021 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 198, 2021 is 1.
HCF(198, 2021) = 1
HCF of 198, 2021 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 198, 2021 is 1.
Highest Common Factor of 198,2021 is 1
Step 1: Since 2021 > 198, we apply the division lemma to 2021 and 198, to get
2021 = 198 x 10 + 41
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 41 and 198, to get
198 = 41 x 4 + 34
Step 3: We consider the new divisor 41 and the new remainder 34, and apply the division lemma to get
41 = 34 x 1 + 7
We consider the new divisor 34 and the new remainder 7,and apply the division lemma to get
34 = 7 x 4 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 198 and 2021 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(34,7) = HCF(41,34) = HCF(198,41) = HCF(2021,198) .
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Frequently Asked Questions on HCF of 198, 2021 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 198, 2021?
Answer: HCF of 198, 2021 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 198, 2021 using Euclid's Algorithm?
Answer: For arbitrary numbers 198, 2021 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.