Highest Common Factor of 8146, 9712 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 8146, 9712 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8146, 9712 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 8146, 9712 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 8146, 9712 is 2.
HCF(8146, 9712) = 2
HCF of 8146, 9712 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8146, 9712 is 2.
Highest Common Factor of 8146,9712 is 2
Step 1: Since 9712 > 8146, we apply the division lemma to 9712 and 8146, to get
9712 = 8146 x 1 + 1566
Step 2: Since the reminder 8146 ≠ 0, we apply division lemma to 1566 and 8146, to get
8146 = 1566 x 5 + 316
Step 3: We consider the new divisor 1566 and the new remainder 316, and apply the division lemma to get
1566 = 316 x 4 + 302
We consider the new divisor 316 and the new remainder 302,and apply the division lemma to get
316 = 302 x 1 + 14
We consider the new divisor 302 and the new remainder 14,and apply the division lemma to get
302 = 14 x 21 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8146 and 9712 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(302,14) = HCF(316,302) = HCF(1566,316) = HCF(8146,1566) = HCF(9712,8146) .
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Frequently Asked Questions on HCF of 8146, 9712 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 8146, 9712?
Answer: HCF of 8146, 9712 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8146, 9712 using Euclid's Algorithm?
Answer: For arbitrary numbers 8146, 9712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.