Highest Common Factor of 677, 51614 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, 51614 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 677, 51614 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, 51614 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, 51614 is 1.
HCF(677, 51614) = 1
HCF of 677, 51614 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, 51614 is 1.
Highest Common Factor of 677,51614 is 1
Step 1: Since 51614 > 677, we apply the division lemma to 51614 and 677, to get
51614 = 677 x 76 + 162
Step 2: Since the reminder 677 ≠ 0, we apply division lemma to 162 and 677, to get
677 = 162 x 4 + 29
Step 3: We consider the new divisor 162 and the new remainder 29, and apply the division lemma to get
162 = 29 x 5 + 17
We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get
29 = 17 x 1 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 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 677 and 51614 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(162,29) = HCF(677,162) = HCF(51614,677) .
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Frequently Asked Questions on HCF of 677, 51614 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, 51614?
Answer: HCF of 677, 51614 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 677, 51614 using Euclid's Algorithm?
Answer: For arbitrary numbers 677, 51614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.