Highest Common Factor of 6768, 710 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 6768, 710 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6768, 710 is 2 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 6768, 710 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 6768, 710 is 2.
HCF(6768, 710) = 2
HCF of 6768, 710 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6768, 710 is 2.
Highest Common Factor of 6768,710 is 2
Step 1: Since 6768 > 710, we apply the division lemma to 6768 and 710, to get
6768 = 710 x 9 + 378
Step 2: Since the reminder 710 ≠ 0, we apply division lemma to 378 and 710, to get
710 = 378 x 1 + 332
Step 3: We consider the new divisor 378 and the new remainder 332, and apply the division lemma to get
378 = 332 x 1 + 46
We consider the new divisor 332 and the new remainder 46,and apply the division lemma to get
332 = 46 x 7 + 10
We consider the new divisor 46 and the new remainder 10,and apply the division lemma to get
46 = 10 x 4 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6768 and 710 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(46,10) = HCF(332,46) = HCF(378,332) = HCF(710,378) = HCF(6768,710) .
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Frequently Asked Questions on HCF of 6768, 710 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 6768, 710?
Answer: HCF of 6768, 710 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6768, 710 using Euclid's Algorithm?
Answer: For arbitrary numbers 6768, 710 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.