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 6101, 3180, 12566 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6101, 3180, 12566 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 6101, 3180, 12566 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 6101, 3180, 12566 is 1.
HCF(6101, 3180, 12566) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6101, 3180, 12566 is 1.
Step 1: Since 6101 > 3180, we apply the division lemma to 6101 and 3180, to get
6101 = 3180 x 1 + 2921
Step 2: Since the reminder 3180 ≠ 0, we apply division lemma to 2921 and 3180, to get
3180 = 2921 x 1 + 259
Step 3: We consider the new divisor 2921 and the new remainder 259, and apply the division lemma to get
2921 = 259 x 11 + 72
We consider the new divisor 259 and the new remainder 72,and apply the division lemma to get
259 = 72 x 3 + 43
We consider the new divisor 72 and the new remainder 43,and apply the division lemma to get
72 = 43 x 1 + 29
We consider the new divisor 43 and the new remainder 29,and apply the division lemma to get
43 = 29 x 1 + 14
We consider the new divisor 29 and the new remainder 14,and apply the division lemma to get
29 = 14 x 2 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6101 and 3180 is 1
Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(43,29) = HCF(72,43) = HCF(259,72) = HCF(2921,259) = HCF(3180,2921) = HCF(6101,3180) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12566 > 1, we apply the division lemma to 12566 and 1, to get
12566 = 1 x 12566 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12566 is 1
Notice that 1 = HCF(12566,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 6101, 3180, 12566?
Answer: HCF of 6101, 3180, 12566 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6101, 3180, 12566 using Euclid's Algorithm?
Answer: For arbitrary numbers 6101, 3180, 12566 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.