Highest Common Factor of 8102, 7582 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, 7582 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8102, 7582 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, 7582 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, 7582 is 2.
HCF(8102, 7582) = 2
HCF of 8102, 7582 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, 7582 is 2.
Highest Common Factor of 8102,7582 is 2
Step 1: Since 8102 > 7582, we apply the division lemma to 8102 and 7582, to get
8102 = 7582 x 1 + 520
Step 2: Since the reminder 7582 ≠ 0, we apply division lemma to 520 and 7582, to get
7582 = 520 x 14 + 302
Step 3: We consider the new divisor 520 and the new remainder 302, and apply the division lemma to get
520 = 302 x 1 + 218
We consider the new divisor 302 and the new remainder 218,and apply the division lemma to get
302 = 218 x 1 + 84
We consider the new divisor 218 and the new remainder 84,and apply the division lemma to get
218 = 84 x 2 + 50
We consider the new divisor 84 and the new remainder 50,and apply the division lemma to get
84 = 50 x 1 + 34
We consider the new divisor 50 and the new remainder 34,and apply the division lemma to get
50 = 34 x 1 + 16
We consider the new divisor 34 and the new remainder 16,and apply the division lemma to get
34 = 16 x 2 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8102 and 7582 is 2
Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(50,34) = HCF(84,50) = HCF(218,84) = HCF(302,218) = HCF(520,302) = HCF(7582,520) = HCF(8102,7582) .
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Frequently Asked Questions on HCF of 8102, 7582 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, 7582?
Answer: HCF of 8102, 7582 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8102, 7582 using Euclid's Algorithm?
Answer: For arbitrary numbers 8102, 7582 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.