Highest Common Factor of 861, 105, 83 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, 105, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 861, 105, 83 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 861, 105, 83 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, 105, 83 is 1.
HCF(861, 105, 83) = 1
HCF of 861, 105, 83 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, 105, 83 is 1.
Highest Common Factor of 861,105,83 is 1
Step 1: Since 861 > 105, we apply the division lemma to 861 and 105, to get
861 = 105 x 8 + 21
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 21 and 105, to get
105 = 21 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 861 and 105 is 21
Notice that 21 = HCF(105,21) = HCF(861,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 83 > 21, we apply the division lemma to 83 and 21, to get
83 = 21 x 3 + 20
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 20 and 21, to get
21 = 20 x 1 + 1
Step 3: We consider the new divisor 20 and the new remainder 1, and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 83 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(83,21) .
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Frequently Asked Questions on HCF of 861, 105, 83 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, 105, 83?
Answer: HCF of 861, 105, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 861, 105, 83 using Euclid's Algorithm?
Answer: For arbitrary numbers 861, 105, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.