Highest Common Factor of 6605, 6744 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 6605, 6744 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6605, 6744 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 6605, 6744 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 6605, 6744 is 1.
HCF(6605, 6744) = 1
HCF of 6605, 6744 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6605, 6744 is 1.
Highest Common Factor of 6605,6744 is 1
Step 1: Since 6744 > 6605, we apply the division lemma to 6744 and 6605, to get
6744 = 6605 x 1 + 139
Step 2: Since the reminder 6605 ≠ 0, we apply division lemma to 139 and 6605, to get
6605 = 139 x 47 + 72
Step 3: We consider the new divisor 139 and the new remainder 72, and apply the division lemma to get
139 = 72 x 1 + 67
We consider the new divisor 72 and the new remainder 67,and apply the division lemma to get
72 = 67 x 1 + 5
We consider the new divisor 67 and the new remainder 5,and apply the division lemma to get
67 = 5 x 13 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 6605 and 6744 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(67,5) = HCF(72,67) = HCF(139,72) = HCF(6605,139) = HCF(6744,6605) .
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Frequently Asked Questions on HCF of 6605, 6744 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 6605, 6744?
Answer: HCF of 6605, 6744 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6605, 6744 using Euclid's Algorithm?
Answer: For arbitrary numbers 6605, 6744 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.