Highest Common Factor of 7970, 8142 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 7970, 8142 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7970, 8142 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 7970, 8142 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 7970, 8142 is 2.
HCF(7970, 8142) = 2
HCF of 7970, 8142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7970, 8142 is 2.
Highest Common Factor of 7970,8142 is 2
Step 1: Since 8142 > 7970, we apply the division lemma to 8142 and 7970, to get
8142 = 7970 x 1 + 172
Step 2: Since the reminder 7970 ≠ 0, we apply division lemma to 172 and 7970, to get
7970 = 172 x 46 + 58
Step 3: We consider the new divisor 172 and the new remainder 58, and apply the division lemma to get
172 = 58 x 2 + 56
We consider the new divisor 58 and the new remainder 56,and apply the division lemma to get
58 = 56 x 1 + 2
We consider the new divisor 56 and the new remainder 2,and apply the division lemma to get
56 = 2 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7970 and 8142 is 2
Notice that 2 = HCF(56,2) = HCF(58,56) = HCF(172,58) = HCF(7970,172) = HCF(8142,7970) .
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Frequently Asked Questions on HCF of 7970, 8142 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 7970, 8142?
Answer: HCF of 7970, 8142 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7970, 8142 using Euclid's Algorithm?
Answer: For arbitrary numbers 7970, 8142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
