Highest Common Factor of 821, 2181 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, 2181 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 2181 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, 2181 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, 2181 is 1.
HCF(821, 2181) = 1
HCF of 821, 2181 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, 2181 is 1.
Highest Common Factor of 821,2181 is 1
Step 1: Since 2181 > 821, we apply the division lemma to 2181 and 821, to get
2181 = 821 x 2 + 539
Step 2: Since the reminder 821 ≠ 0, we apply division lemma to 539 and 821, to get
821 = 539 x 1 + 282
Step 3: We consider the new divisor 539 and the new remainder 282, and apply the division lemma to get
539 = 282 x 1 + 257
We consider the new divisor 282 and the new remainder 257,and apply the division lemma to get
282 = 257 x 1 + 25
We consider the new divisor 257 and the new remainder 25,and apply the division lemma to get
257 = 25 x 10 + 7
We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get
25 = 7 x 3 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 2181 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(257,25) = HCF(282,257) = HCF(539,282) = HCF(821,539) = HCF(2181,821) .
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Frequently Asked Questions on HCF of 821, 2181 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, 2181?
Answer: HCF of 821, 2181 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 2181 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 2181 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.