Highest Common Factor of 2346, 6172 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 2346, 6172 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2346, 6172 is 2 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 2346, 6172 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 2346, 6172 is 2.
HCF(2346, 6172) = 2
HCF of 2346, 6172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2346, 6172 is 2.
Highest Common Factor of 2346,6172 is 2
Step 1: Since 6172 > 2346, we apply the division lemma to 6172 and 2346, to get
6172 = 2346 x 2 + 1480
Step 2: Since the reminder 2346 ≠ 0, we apply division lemma to 1480 and 2346, to get
2346 = 1480 x 1 + 866
Step 3: We consider the new divisor 1480 and the new remainder 866, and apply the division lemma to get
1480 = 866 x 1 + 614
We consider the new divisor 866 and the new remainder 614,and apply the division lemma to get
866 = 614 x 1 + 252
We consider the new divisor 614 and the new remainder 252,and apply the division lemma to get
614 = 252 x 2 + 110
We consider the new divisor 252 and the new remainder 110,and apply the division lemma to get
252 = 110 x 2 + 32
We consider the new divisor 110 and the new remainder 32,and apply the division lemma to get
110 = 32 x 3 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2346 and 6172 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(110,32) = HCF(252,110) = HCF(614,252) = HCF(866,614) = HCF(1480,866) = HCF(2346,1480) = HCF(6172,2346) .
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Frequently Asked Questions on HCF of 2346, 6172 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 2346, 6172?
Answer: HCF of 2346, 6172 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2346, 6172 using Euclid's Algorithm?
Answer: For arbitrary numbers 2346, 6172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.