Highest Common Factor of 686, 382, 655 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 686, 382, 655 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 382, 655 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 686, 382, 655 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 686, 382, 655 is 1.
HCF(686, 382, 655) = 1
HCF of 686, 382, 655 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 686, 382, 655 is 1.
Highest Common Factor of 686,382,655 is 1
Step 1: Since 686 > 382, we apply the division lemma to 686 and 382, to get
686 = 382 x 1 + 304
Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 304 and 382, to get
382 = 304 x 1 + 78
Step 3: We consider the new divisor 304 and the new remainder 78, and apply the division lemma to get
304 = 78 x 3 + 70
We consider the new divisor 78 and the new remainder 70,and apply the division lemma to get
78 = 70 x 1 + 8
We consider the new divisor 70 and the new remainder 8,and apply the division lemma to get
70 = 8 x 8 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 686 and 382 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(70,8) = HCF(78,70) = HCF(304,78) = HCF(382,304) = HCF(686,382) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 655 > 2, we apply the division lemma to 655 and 2, to get
655 = 2 x 327 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 655 is 1
Notice that 1 = HCF(2,1) = HCF(655,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 686, 382, 655 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 686, 382, 655?
Answer: HCF of 686, 382, 655 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 382, 655 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 382, 655 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
