Highest Common Factor of 681, 861 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 681, 861 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 681, 861 is 3 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 681, 861 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 681, 861 is 3.
HCF(681, 861) = 3
HCF of 681, 861 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 681, 861 is 3.
Highest Common Factor of 681,861 is 3
Step 1: Since 861 > 681, we apply the division lemma to 861 and 681, to get
861 = 681 x 1 + 180
Step 2: Since the reminder 681 ≠ 0, we apply division lemma to 180 and 681, to get
681 = 180 x 3 + 141
Step 3: We consider the new divisor 180 and the new remainder 141, and apply the division lemma to get
180 = 141 x 1 + 39
We consider the new divisor 141 and the new remainder 39,and apply the division lemma to get
141 = 39 x 3 + 24
We consider the new divisor 39 and the new remainder 24,and apply the division lemma to get
39 = 24 x 1 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 681 and 861 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(141,39) = HCF(180,141) = HCF(681,180) = HCF(861,681) .
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Frequently Asked Questions on HCF of 681, 861 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 681, 861?
Answer: HCF of 681, 861 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 681, 861 using Euclid's Algorithm?
Answer: For arbitrary numbers 681, 861 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.