Highest Common Factor of 8102, 1734 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 8102, 1734 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8102, 1734 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 8102, 1734 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 8102, 1734 is 2.
HCF(8102, 1734) = 2
HCF of 8102, 1734 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8102, 1734 is 2.
Highest Common Factor of 8102,1734 is 2
Step 1: Since 8102 > 1734, we apply the division lemma to 8102 and 1734, to get
8102 = 1734 x 4 + 1166
Step 2: Since the reminder 1734 ≠ 0, we apply division lemma to 1166 and 1734, to get
1734 = 1166 x 1 + 568
Step 3: We consider the new divisor 1166 and the new remainder 568, and apply the division lemma to get
1166 = 568 x 2 + 30
We consider the new divisor 568 and the new remainder 30,and apply the division lemma to get
568 = 30 x 18 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8102 and 1734 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(568,30) = HCF(1166,568) = HCF(1734,1166) = HCF(8102,1734) .
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Frequently Asked Questions on HCF of 8102, 1734 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 8102, 1734?
Answer: HCF of 8102, 1734 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8102, 1734 using Euclid's Algorithm?
Answer: For arbitrary numbers 8102, 1734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
