Highest Common Factor of 723, 6761 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 723, 6761 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 6761 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 723, 6761 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 723, 6761 is 1.
HCF(723, 6761) = 1
HCF of 723, 6761 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 723, 6761 is 1.
Highest Common Factor of 723,6761 is 1
Step 1: Since 6761 > 723, we apply the division lemma to 6761 and 723, to get
6761 = 723 x 9 + 254
Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 254 and 723, to get
723 = 254 x 2 + 215
Step 3: We consider the new divisor 254 and the new remainder 215, and apply the division lemma to get
254 = 215 x 1 + 39
We consider the new divisor 215 and the new remainder 39,and apply the division lemma to get
215 = 39 x 5 + 20
We consider the new divisor 39 and the new remainder 20,and apply the division lemma to get
39 = 20 x 1 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 723 and 6761 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(39,20) = HCF(215,39) = HCF(254,215) = HCF(723,254) = HCF(6761,723) .
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Frequently Asked Questions on HCF of 723, 6761 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 723, 6761?
Answer: HCF of 723, 6761 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 6761 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 6761 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
