Highest Common Factor of 971, 689 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 971, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 971, 689 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 971, 689 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 971, 689 is 1.
HCF(971, 689) = 1
HCF of 971, 689 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 971, 689 is 1.
Highest Common Factor of 971,689 is 1
Step 1: Since 971 > 689, we apply the division lemma to 971 and 689, to get
971 = 689 x 1 + 282
Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 282 and 689, to get
689 = 282 x 2 + 125
Step 3: We consider the new divisor 282 and the new remainder 125, and apply the division lemma to get
282 = 125 x 2 + 32
We consider the new divisor 125 and the new remainder 32,and apply the division lemma to get
125 = 32 x 3 + 29
We consider the new divisor 32 and the new remainder 29,and apply the division lemma to get
32 = 29 x 1 + 3
We consider the new divisor 29 and the new remainder 3,and apply the division lemma to get
29 = 3 x 9 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 971 and 689 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(29,3) = HCF(32,29) = HCF(125,32) = HCF(282,125) = HCF(689,282) = HCF(971,689) .
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Frequently Asked Questions on HCF of 971, 689 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 971, 689?
Answer: HCF of 971, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 971, 689 using Euclid's Algorithm?
Answer: For arbitrary numbers 971, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.