Highest Common Factor of 8657, 5940 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 8657, 5940 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 8657, 5940 is 11 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 8657, 5940 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 8657, 5940 is 11.
HCF(8657, 5940) = 11
HCF of 8657, 5940 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8657, 5940 is 11.
Highest Common Factor of 8657,5940 is 11
Step 1: Since 8657 > 5940, we apply the division lemma to 8657 and 5940, to get
8657 = 5940 x 1 + 2717
Step 2: Since the reminder 5940 ≠ 0, we apply division lemma to 2717 and 5940, to get
5940 = 2717 x 2 + 506
Step 3: We consider the new divisor 2717 and the new remainder 506, and apply the division lemma to get
2717 = 506 x 5 + 187
We consider the new divisor 506 and the new remainder 187,and apply the division lemma to get
506 = 187 x 2 + 132
We consider the new divisor 187 and the new remainder 132,and apply the division lemma to get
187 = 132 x 1 + 55
We consider the new divisor 132 and the new remainder 55,and apply the division lemma to get
132 = 55 x 2 + 22
We consider the new divisor 55 and the new remainder 22,and apply the division lemma to get
55 = 22 x 2 + 11
We consider the new divisor 22 and the new remainder 11,and apply the division lemma to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 8657 and 5940 is 11
Notice that 11 = HCF(22,11) = HCF(55,22) = HCF(132,55) = HCF(187,132) = HCF(506,187) = HCF(2717,506) = HCF(5940,2717) = HCF(8657,5940) .
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Frequently Asked Questions on HCF of 8657, 5940 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 8657, 5940?
Answer: HCF of 8657, 5940 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8657, 5940 using Euclid's Algorithm?
Answer: For arbitrary numbers 8657, 5940 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.