Highest Common Factor of 821, 637, 231 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 821, 637, 231 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 637, 231 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 821, 637, 231 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 821, 637, 231 is 1.
HCF(821, 637, 231) = 1
HCF of 821, 637, 231 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 637, 231 is 1.
Highest Common Factor of 821,637,231 is 1
Step 1: Since 821 > 637, we apply the division lemma to 821 and 637, to get
821 = 637 x 1 + 184
Step 2: Since the reminder 637 ≠ 0, we apply division lemma to 184 and 637, to get
637 = 184 x 3 + 85
Step 3: We consider the new divisor 184 and the new remainder 85, and apply the division lemma to get
184 = 85 x 2 + 14
We consider the new divisor 85 and the new remainder 14,and apply the division lemma to get
85 = 14 x 6 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 637 is 1
Notice that 1 = HCF(14,1) = HCF(85,14) = HCF(184,85) = HCF(637,184) = HCF(821,637) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 231 > 1, we apply the division lemma to 231 and 1, to get
231 = 1 x 231 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 231 is 1
Notice that 1 = HCF(231,1) .
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Frequently Asked Questions on HCF of 821, 637, 231 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 821, 637, 231?
Answer: HCF of 821, 637, 231 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 637, 231 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 637, 231 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.