Highest Common Factor of 861, 519 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 861, 519 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 861, 519 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 861, 519 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 861, 519 is 3.
HCF(861, 519) = 3
HCF of 861, 519 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 861, 519 is 3.
Highest Common Factor of 861,519 is 3
Step 1: Since 861 > 519, we apply the division lemma to 861 and 519, to get
861 = 519 x 1 + 342
Step 2: Since the reminder 519 ≠ 0, we apply division lemma to 342 and 519, to get
519 = 342 x 1 + 177
Step 3: We consider the new divisor 342 and the new remainder 177, and apply the division lemma to get
342 = 177 x 1 + 165
We consider the new divisor 177 and the new remainder 165,and apply the division lemma to get
177 = 165 x 1 + 12
We consider the new divisor 165 and the new remainder 12,and apply the division lemma to get
165 = 12 x 13 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 861 and 519 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(165,12) = HCF(177,165) = HCF(342,177) = HCF(519,342) = HCF(861,519) .
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Frequently Asked Questions on HCF of 861, 519 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 861, 519?
Answer: HCF of 861, 519 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 861, 519 using Euclid's Algorithm?
Answer: For arbitrary numbers 861, 519 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.