Highest Common Factor of 921, 5122 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 921, 5122 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 921, 5122 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 921, 5122 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 921, 5122 is 1.
HCF(921, 5122) = 1
HCF of 921, 5122 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 921, 5122 is 1.
Highest Common Factor of 921,5122 is 1
Step 1: Since 5122 > 921, we apply the division lemma to 5122 and 921, to get
5122 = 921 x 5 + 517
Step 2: Since the reminder 921 ≠ 0, we apply division lemma to 517 and 921, to get
921 = 517 x 1 + 404
Step 3: We consider the new divisor 517 and the new remainder 404, and apply the division lemma to get
517 = 404 x 1 + 113
We consider the new divisor 404 and the new remainder 113,and apply the division lemma to get
404 = 113 x 3 + 65
We consider the new divisor 113 and the new remainder 65,and apply the division lemma to get
113 = 65 x 1 + 48
We consider the new divisor 65 and the new remainder 48,and apply the division lemma to get
65 = 48 x 1 + 17
We consider the new divisor 48 and the new remainder 17,and apply the division lemma to get
48 = 17 x 2 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 921 and 5122 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(48,17) = HCF(65,48) = HCF(113,65) = HCF(404,113) = HCF(517,404) = HCF(921,517) = HCF(5122,921) .
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Frequently Asked Questions on HCF of 921, 5122 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 921, 5122?
Answer: HCF of 921, 5122 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 921, 5122 using Euclid's Algorithm?
Answer: For arbitrary numbers 921, 5122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.