Highest Common Factor of 717, 21211 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 717, 21211 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 717, 21211 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 717, 21211 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 717, 21211 is 1.
HCF(717, 21211) = 1
HCF of 717, 21211 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 717, 21211 is 1.
Highest Common Factor of 717,21211 is 1
Step 1: Since 21211 > 717, we apply the division lemma to 21211 and 717, to get
21211 = 717 x 29 + 418
Step 2: Since the reminder 717 ≠ 0, we apply division lemma to 418 and 717, to get
717 = 418 x 1 + 299
Step 3: We consider the new divisor 418 and the new remainder 299, and apply the division lemma to get
418 = 299 x 1 + 119
We consider the new divisor 299 and the new remainder 119,and apply the division lemma to get
299 = 119 x 2 + 61
We consider the new divisor 119 and the new remainder 61,and apply the division lemma to get
119 = 61 x 1 + 58
We consider the new divisor 61 and the new remainder 58,and apply the division lemma to get
61 = 58 x 1 + 3
We consider the new divisor 58 and the new remainder 3,and apply the division lemma to get
58 = 3 x 19 + 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 717 and 21211 is 1
Notice that 1 = HCF(3,1) = HCF(58,3) = HCF(61,58) = HCF(119,61) = HCF(299,119) = HCF(418,299) = HCF(717,418) = HCF(21211,717) .
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Frequently Asked Questions on HCF of 717, 21211 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 717, 21211?
Answer: HCF of 717, 21211 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 717, 21211 using Euclid's Algorithm?
Answer: For arbitrary numbers 717, 21211 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.