Highest Common Factor of 8772, 7611, 71251 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 8772, 7611, 71251 i.e. 43 the largest integer that leaves a remainder zero for all numbers.
HCF of 8772, 7611, 71251 is 43 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 8772, 7611, 71251 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 8772, 7611, 71251 is 43.
HCF(8772, 7611, 71251) = 43
HCF of 8772, 7611, 71251 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8772, 7611, 71251 is 43.
Highest Common Factor of 8772,7611,71251 is 43
Step 1: Since 8772 > 7611, we apply the division lemma to 8772 and 7611, to get
8772 = 7611 x 1 + 1161
Step 2: Since the reminder 7611 ≠ 0, we apply division lemma to 1161 and 7611, to get
7611 = 1161 x 6 + 645
Step 3: We consider the new divisor 1161 and the new remainder 645, and apply the division lemma to get
1161 = 645 x 1 + 516
We consider the new divisor 645 and the new remainder 516,and apply the division lemma to get
645 = 516 x 1 + 129
We consider the new divisor 516 and the new remainder 129,and apply the division lemma to get
516 = 129 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 129, the HCF of 8772 and 7611 is 129
Notice that 129 = HCF(516,129) = HCF(645,516) = HCF(1161,645) = HCF(7611,1161) = HCF(8772,7611) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 71251 > 129, we apply the division lemma to 71251 and 129, to get
71251 = 129 x 552 + 43
Step 2: Since the reminder 129 ≠ 0, we apply division lemma to 43 and 129, to get
129 = 43 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 129 and 71251 is 43
Notice that 43 = HCF(129,43) = HCF(71251,129) .
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Frequently Asked Questions on HCF of 8772, 7611, 71251 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 8772, 7611, 71251?
Answer: HCF of 8772, 7611, 71251 is 43 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8772, 7611, 71251 using Euclid's Algorithm?
Answer: For arbitrary numbers 8772, 7611, 71251 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.