Highest Common Factor of 8221, 857 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 8221, 857 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8221, 857 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 8221, 857 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 8221, 857 is 1.
HCF(8221, 857) = 1
HCF of 8221, 857 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8221, 857 is 1.
Highest Common Factor of 8221,857 is 1
Step 1: Since 8221 > 857, we apply the division lemma to 8221 and 857, to get
8221 = 857 x 9 + 508
Step 2: Since the reminder 857 ≠ 0, we apply division lemma to 508 and 857, to get
857 = 508 x 1 + 349
Step 3: We consider the new divisor 508 and the new remainder 349, and apply the division lemma to get
508 = 349 x 1 + 159
We consider the new divisor 349 and the new remainder 159,and apply the division lemma to get
349 = 159 x 2 + 31
We consider the new divisor 159 and the new remainder 31,and apply the division lemma to get
159 = 31 x 5 + 4
We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get
31 = 4 x 7 + 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 8221 and 857 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(159,31) = HCF(349,159) = HCF(508,349) = HCF(857,508) = HCF(8221,857) .
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Frequently Asked Questions on HCF of 8221, 857 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 8221, 857?
Answer: HCF of 8221, 857 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8221, 857 using Euclid's Algorithm?
Answer: For arbitrary numbers 8221, 857 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
