Highest Common Factor of 9117, 4961, 27106 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 9117, 4961, 27106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9117, 4961, 27106 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 9117, 4961, 27106 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 9117, 4961, 27106 is 1.
HCF(9117, 4961, 27106) = 1
HCF of 9117, 4961, 27106 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9117, 4961, 27106 is 1.
Highest Common Factor of 9117,4961,27106 is 1
Step 1: Since 9117 > 4961, we apply the division lemma to 9117 and 4961, to get
9117 = 4961 x 1 + 4156
Step 2: Since the reminder 4961 ≠ 0, we apply division lemma to 4156 and 4961, to get
4961 = 4156 x 1 + 805
Step 3: We consider the new divisor 4156 and the new remainder 805, and apply the division lemma to get
4156 = 805 x 5 + 131
We consider the new divisor 805 and the new remainder 131,and apply the division lemma to get
805 = 131 x 6 + 19
We consider the new divisor 131 and the new remainder 19,and apply the division lemma to get
131 = 19 x 6 + 17
We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get
19 = 17 x 1 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 9117 and 4961 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(131,19) = HCF(805,131) = HCF(4156,805) = HCF(4961,4156) = HCF(9117,4961) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 27106 > 1, we apply the division lemma to 27106 and 1, to get
27106 = 1 x 27106 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 27106 is 1
Notice that 1 = HCF(27106,1) .
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Frequently Asked Questions on HCF of 9117, 4961, 27106 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 9117, 4961, 27106?
Answer: HCF of 9117, 4961, 27106 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9117, 4961, 27106 using Euclid's Algorithm?
Answer: For arbitrary numbers 9117, 4961, 27106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.