Highest Common Factor of 8730, 6171, 65388 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 8730, 6171, 65388 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8730, 6171, 65388 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 8730, 6171, 65388 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 8730, 6171, 65388 is 3.
HCF(8730, 6171, 65388) = 3
HCF of 8730, 6171, 65388 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8730, 6171, 65388 is 3.
Highest Common Factor of 8730,6171,65388 is 3
Step 1: Since 8730 > 6171, we apply the division lemma to 8730 and 6171, to get
8730 = 6171 x 1 + 2559
Step 2: Since the reminder 6171 ≠ 0, we apply division lemma to 2559 and 6171, to get
6171 = 2559 x 2 + 1053
Step 3: We consider the new divisor 2559 and the new remainder 1053, and apply the division lemma to get
2559 = 1053 x 2 + 453
We consider the new divisor 1053 and the new remainder 453,and apply the division lemma to get
1053 = 453 x 2 + 147
We consider the new divisor 453 and the new remainder 147,and apply the division lemma to get
453 = 147 x 3 + 12
We consider the new divisor 147 and the new remainder 12,and apply the division lemma to get
147 = 12 x 12 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8730 and 6171 is 3
Notice that 3 = HCF(12,3) = HCF(147,12) = HCF(453,147) = HCF(1053,453) = HCF(2559,1053) = HCF(6171,2559) = HCF(8730,6171) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65388 > 3, we apply the division lemma to 65388 and 3, to get
65388 = 3 x 21796 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 65388 is 3
Notice that 3 = HCF(65388,3) .
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Frequently Asked Questions on HCF of 8730, 6171, 65388 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 8730, 6171, 65388?
Answer: HCF of 8730, 6171, 65388 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8730, 6171, 65388 using Euclid's Algorithm?
Answer: For arbitrary numbers 8730, 6171, 65388 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.