Highest Common Factor of 8714, 7162 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 8714, 7162 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8714, 7162 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 8714, 7162 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 8714, 7162 is 2.
HCF(8714, 7162) = 2
HCF of 8714, 7162 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8714, 7162 is 2.
Highest Common Factor of 8714,7162 is 2
Step 1: Since 8714 > 7162, we apply the division lemma to 8714 and 7162, to get
8714 = 7162 x 1 + 1552
Step 2: Since the reminder 7162 ≠ 0, we apply division lemma to 1552 and 7162, to get
7162 = 1552 x 4 + 954
Step 3: We consider the new divisor 1552 and the new remainder 954, and apply the division lemma to get
1552 = 954 x 1 + 598
We consider the new divisor 954 and the new remainder 598,and apply the division lemma to get
954 = 598 x 1 + 356
We consider the new divisor 598 and the new remainder 356,and apply the division lemma to get
598 = 356 x 1 + 242
We consider the new divisor 356 and the new remainder 242,and apply the division lemma to get
356 = 242 x 1 + 114
We consider the new divisor 242 and the new remainder 114,and apply the division lemma to get
242 = 114 x 2 + 14
We consider the new divisor 114 and the new remainder 14,and apply the division lemma to get
114 = 14 x 8 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8714 and 7162 is 2
Notice that 2 = HCF(14,2) = HCF(114,14) = HCF(242,114) = HCF(356,242) = HCF(598,356) = HCF(954,598) = HCF(1552,954) = HCF(7162,1552) = HCF(8714,7162) .
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Frequently Asked Questions on HCF of 8714, 7162 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 8714, 7162?
Answer: HCF of 8714, 7162 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8714, 7162 using Euclid's Algorithm?
Answer: For arbitrary numbers 8714, 7162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.