Highest Common Factor of 2745, 6686 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 2745, 6686 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2745, 6686 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 2745, 6686 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 2745, 6686 is 1.
HCF(2745, 6686) = 1
HCF of 2745, 6686 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2745, 6686 is 1.
Highest Common Factor of 2745,6686 is 1
Step 1: Since 6686 > 2745, we apply the division lemma to 6686 and 2745, to get
6686 = 2745 x 2 + 1196
Step 2: Since the reminder 2745 ≠ 0, we apply division lemma to 1196 and 2745, to get
2745 = 1196 x 2 + 353
Step 3: We consider the new divisor 1196 and the new remainder 353, and apply the division lemma to get
1196 = 353 x 3 + 137
We consider the new divisor 353 and the new remainder 137,and apply the division lemma to get
353 = 137 x 2 + 79
We consider the new divisor 137 and the new remainder 79,and apply the division lemma to get
137 = 79 x 1 + 58
We consider the new divisor 79 and the new remainder 58,and apply the division lemma to get
79 = 58 x 1 + 21
We consider the new divisor 58 and the new remainder 21,and apply the division lemma to get
58 = 21 x 2 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2745 and 6686 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(58,21) = HCF(79,58) = HCF(137,79) = HCF(353,137) = HCF(1196,353) = HCF(2745,1196) = HCF(6686,2745) .
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Frequently Asked Questions on HCF of 2745, 6686 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 2745, 6686?
Answer: HCF of 2745, 6686 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2745, 6686 using Euclid's Algorithm?
Answer: For arbitrary numbers 2745, 6686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.