Highest Common Factor of 838, 21637 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 838, 21637 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 838, 21637 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 838, 21637 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 838, 21637 is 1.
HCF(838, 21637) = 1
HCF of 838, 21637 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 838, 21637 is 1.
Highest Common Factor of 838,21637 is 1
Step 1: Since 21637 > 838, we apply the division lemma to 21637 and 838, to get
21637 = 838 x 25 + 687
Step 2: Since the reminder 838 ≠ 0, we apply division lemma to 687 and 838, to get
838 = 687 x 1 + 151
Step 3: We consider the new divisor 687 and the new remainder 151, and apply the division lemma to get
687 = 151 x 4 + 83
We consider the new divisor 151 and the new remainder 83,and apply the division lemma to get
151 = 83 x 1 + 68
We consider the new divisor 83 and the new remainder 68,and apply the division lemma to get
83 = 68 x 1 + 15
We consider the new divisor 68 and the new remainder 15,and apply the division lemma to get
68 = 15 x 4 + 8
We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get
15 = 8 x 1 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 838 and 21637 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(68,15) = HCF(83,68) = HCF(151,83) = HCF(687,151) = HCF(838,687) = HCF(21637,838) .
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Frequently Asked Questions on HCF of 838, 21637 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 838, 21637?
Answer: HCF of 838, 21637 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 838, 21637 using Euclid's Algorithm?
Answer: For arbitrary numbers 838, 21637 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.