Highest Common Factor of 8601, 7728 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 8601, 7728 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8601, 7728 is 3 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 8601, 7728 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 8601, 7728 is 3.
HCF(8601, 7728) = 3
HCF of 8601, 7728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8601, 7728 is 3.
Highest Common Factor of 8601,7728 is 3
Step 1: Since 8601 > 7728, we apply the division lemma to 8601 and 7728, to get
8601 = 7728 x 1 + 873
Step 2: Since the reminder 7728 ≠ 0, we apply division lemma to 873 and 7728, to get
7728 = 873 x 8 + 744
Step 3: We consider the new divisor 873 and the new remainder 744, and apply the division lemma to get
873 = 744 x 1 + 129
We consider the new divisor 744 and the new remainder 129,and apply the division lemma to get
744 = 129 x 5 + 99
We consider the new divisor 129 and the new remainder 99,and apply the division lemma to get
129 = 99 x 1 + 30
We consider the new divisor 99 and the new remainder 30,and apply the division lemma to get
99 = 30 x 3 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8601 and 7728 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(99,30) = HCF(129,99) = HCF(744,129) = HCF(873,744) = HCF(7728,873) = HCF(8601,7728) .
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Frequently Asked Questions on HCF of 8601, 7728 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 8601, 7728?
Answer: HCF of 8601, 7728 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8601, 7728 using Euclid's Algorithm?
Answer: For arbitrary numbers 8601, 7728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
