Highest Common Factor of 274, 2639, 6788 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 274, 2639, 6788 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 274, 2639, 6788 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 274, 2639, 6788 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 274, 2639, 6788 is 1.
HCF(274, 2639, 6788) = 1
HCF of 274, 2639, 6788 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 274, 2639, 6788 is 1.
Highest Common Factor of 274,2639,6788 is 1
Step 1: Since 2639 > 274, we apply the division lemma to 2639 and 274, to get
2639 = 274 x 9 + 173
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 173 and 274, to get
274 = 173 x 1 + 101
Step 3: We consider the new divisor 173 and the new remainder 101, and apply the division lemma to get
173 = 101 x 1 + 72
We consider the new divisor 101 and the new remainder 72,and apply the division lemma to get
101 = 72 x 1 + 29
We consider the new divisor 72 and the new remainder 29,and apply the division lemma to get
72 = 29 x 2 + 14
We consider the new divisor 29 and the new remainder 14,and apply the division lemma to get
29 = 14 x 2 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 274 and 2639 is 1
Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(72,29) = HCF(101,72) = HCF(173,101) = HCF(274,173) = HCF(2639,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6788 > 1, we apply the division lemma to 6788 and 1, to get
6788 = 1 x 6788 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6788 is 1
Notice that 1 = HCF(6788,1) .
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Frequently Asked Questions on HCF of 274, 2639, 6788 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 274, 2639, 6788?
Answer: HCF of 274, 2639, 6788 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 274, 2639, 6788 using Euclid's Algorithm?
Answer: For arbitrary numbers 274, 2639, 6788 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.