Highest Common Factor of 7102, 8362 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 7102, 8362 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7102, 8362 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 7102, 8362 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 7102, 8362 is 2.
HCF(7102, 8362) = 2
HCF of 7102, 8362 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7102, 8362 is 2.
Highest Common Factor of 7102,8362 is 2
Step 1: Since 8362 > 7102, we apply the division lemma to 8362 and 7102, to get
8362 = 7102 x 1 + 1260
Step 2: Since the reminder 7102 ≠ 0, we apply division lemma to 1260 and 7102, to get
7102 = 1260 x 5 + 802
Step 3: We consider the new divisor 1260 and the new remainder 802, and apply the division lemma to get
1260 = 802 x 1 + 458
We consider the new divisor 802 and the new remainder 458,and apply the division lemma to get
802 = 458 x 1 + 344
We consider the new divisor 458 and the new remainder 344,and apply the division lemma to get
458 = 344 x 1 + 114
We consider the new divisor 344 and the new remainder 114,and apply the division lemma to get
344 = 114 x 3 + 2
We consider the new divisor 114 and the new remainder 2,and apply the division lemma to get
114 = 2 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7102 and 8362 is 2
Notice that 2 = HCF(114,2) = HCF(344,114) = HCF(458,344) = HCF(802,458) = HCF(1260,802) = HCF(7102,1260) = HCF(8362,7102) .
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Frequently Asked Questions on HCF of 7102, 8362 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 7102, 8362?
Answer: HCF of 7102, 8362 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7102, 8362 using Euclid's Algorithm?
Answer: For arbitrary numbers 7102, 8362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.