Highest Common Factor of 677, 5135 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 677, 5135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 677, 5135 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 677, 5135 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 677, 5135 is 1.
HCF(677, 5135) = 1
HCF of 677, 5135 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 677, 5135 is 1.
Highest Common Factor of 677,5135 is 1
Step 1: Since 5135 > 677, we apply the division lemma to 5135 and 677, to get
5135 = 677 x 7 + 396
Step 2: Since the reminder 677 ≠ 0, we apply division lemma to 396 and 677, to get
677 = 396 x 1 + 281
Step 3: We consider the new divisor 396 and the new remainder 281, and apply the division lemma to get
396 = 281 x 1 + 115
We consider the new divisor 281 and the new remainder 115,and apply the division lemma to get
281 = 115 x 2 + 51
We consider the new divisor 115 and the new remainder 51,and apply the division lemma to get
115 = 51 x 2 + 13
We consider the new divisor 51 and the new remainder 13,and apply the division lemma to get
51 = 13 x 3 + 12
We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get
13 = 12 x 1 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 677 and 5135 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(51,13) = HCF(115,51) = HCF(281,115) = HCF(396,281) = HCF(677,396) = HCF(5135,677) .
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Frequently Asked Questions on HCF of 677, 5135 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 677, 5135?
Answer: HCF of 677, 5135 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 677, 5135 using Euclid's Algorithm?
Answer: For arbitrary numbers 677, 5135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.