Highest Common Factor of 6971, 685 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 6971, 685 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6971, 685 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 6971, 685 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 6971, 685 is 1.
HCF(6971, 685) = 1
HCF of 6971, 685 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6971, 685 is 1.
Highest Common Factor of 6971,685 is 1
Step 1: Since 6971 > 685, we apply the division lemma to 6971 and 685, to get
6971 = 685 x 10 + 121
Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 121 and 685, to get
685 = 121 x 5 + 80
Step 3: We consider the new divisor 121 and the new remainder 80, and apply the division lemma to get
121 = 80 x 1 + 41
We consider the new divisor 80 and the new remainder 41,and apply the division lemma to get
80 = 41 x 1 + 39
We consider the new divisor 41 and the new remainder 39,and apply the division lemma to get
41 = 39 x 1 + 2
We consider the new divisor 39 and the new remainder 2,and apply the division lemma to get
39 = 2 x 19 + 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 6971 and 685 is 1
Notice that 1 = HCF(2,1) = HCF(39,2) = HCF(41,39) = HCF(80,41) = HCF(121,80) = HCF(685,121) = HCF(6971,685) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 6971, 685 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 6971, 685?
Answer: HCF of 6971, 685 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6971, 685 using Euclid's Algorithm?
Answer: For arbitrary numbers 6971, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.