Highest Common Factor of 6817, 7722 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 6817, 7722 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6817, 7722 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 6817, 7722 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 6817, 7722 is 1.
HCF(6817, 7722) = 1
HCF of 6817, 7722 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6817, 7722 is 1.
Highest Common Factor of 6817,7722 is 1
Step 1: Since 7722 > 6817, we apply the division lemma to 7722 and 6817, to get
7722 = 6817 x 1 + 905
Step 2: Since the reminder 6817 ≠ 0, we apply division lemma to 905 and 6817, to get
6817 = 905 x 7 + 482
Step 3: We consider the new divisor 905 and the new remainder 482, and apply the division lemma to get
905 = 482 x 1 + 423
We consider the new divisor 482 and the new remainder 423,and apply the division lemma to get
482 = 423 x 1 + 59
We consider the new divisor 423 and the new remainder 59,and apply the division lemma to get
423 = 59 x 7 + 10
We consider the new divisor 59 and the new remainder 10,and apply the division lemma to get
59 = 10 x 5 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6817 and 7722 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(59,10) = HCF(423,59) = HCF(482,423) = HCF(905,482) = HCF(6817,905) = HCF(7722,6817) .
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Frequently Asked Questions on HCF of 6817, 7722 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 6817, 7722?
Answer: HCF of 6817, 7722 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6817, 7722 using Euclid's Algorithm?
Answer: For arbitrary numbers 6817, 7722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.