Highest Common Factor of 7872, 8630 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 7872, 8630 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7872, 8630 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 7872, 8630 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 7872, 8630 is 2.
HCF(7872, 8630) = 2
HCF of 7872, 8630 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7872, 8630 is 2.
Highest Common Factor of 7872,8630 is 2
Step 1: Since 8630 > 7872, we apply the division lemma to 8630 and 7872, to get
8630 = 7872 x 1 + 758
Step 2: Since the reminder 7872 ≠ 0, we apply division lemma to 758 and 7872, to get
7872 = 758 x 10 + 292
Step 3: We consider the new divisor 758 and the new remainder 292, and apply the division lemma to get
758 = 292 x 2 + 174
We consider the new divisor 292 and the new remainder 174,and apply the division lemma to get
292 = 174 x 1 + 118
We consider the new divisor 174 and the new remainder 118,and apply the division lemma to get
174 = 118 x 1 + 56
We consider the new divisor 118 and the new remainder 56,and apply the division lemma to get
118 = 56 x 2 + 6
We consider the new divisor 56 and the new remainder 6,and apply the division lemma to get
56 = 6 x 9 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7872 and 8630 is 2
Notice that 2 = HCF(6,2) = HCF(56,6) = HCF(118,56) = HCF(174,118) = HCF(292,174) = HCF(758,292) = HCF(7872,758) = HCF(8630,7872) .
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Frequently Asked Questions on HCF of 7872, 8630 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 7872, 8630?
Answer: HCF of 7872, 8630 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7872, 8630 using Euclid's Algorithm?
Answer: For arbitrary numbers 7872, 8630 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.