Highest Common Factor of 689, 961 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 689, 961 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 689, 961 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 689, 961 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 689, 961 is 1.
HCF(689, 961) = 1
HCF of 689, 961 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 689, 961 is 1.
Highest Common Factor of 689,961 is 1
Step 1: Since 961 > 689, we apply the division lemma to 961 and 689, to get
961 = 689 x 1 + 272
Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 272 and 689, to get
689 = 272 x 2 + 145
Step 3: We consider the new divisor 272 and the new remainder 145, and apply the division lemma to get
272 = 145 x 1 + 127
We consider the new divisor 145 and the new remainder 127,and apply the division lemma to get
145 = 127 x 1 + 18
We consider the new divisor 127 and the new remainder 18,and apply the division lemma to get
127 = 18 x 7 + 1
We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get
18 = 1 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 689 and 961 is 1
Notice that 1 = HCF(18,1) = HCF(127,18) = HCF(145,127) = HCF(272,145) = HCF(689,272) = HCF(961,689) .
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Frequently Asked Questions on HCF of 689, 961 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 689, 961?
Answer: HCF of 689, 961 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 689, 961 using Euclid's Algorithm?
Answer: For arbitrary numbers 689, 961 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.