Highest Common Factor of 871, 537, 680 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 871, 537, 680 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 871, 537, 680 is 1 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 871, 537, 680 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 871, 537, 680 is 1.
HCF(871, 537, 680) = 1
HCF of 871, 537, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 871, 537, 680 is 1.
Highest Common Factor of 871,537,680 is 1
Step 1: Since 871 > 537, we apply the division lemma to 871 and 537, to get
871 = 537 x 1 + 334
Step 2: Since the reminder 537 ≠ 0, we apply division lemma to 334 and 537, to get
537 = 334 x 1 + 203
Step 3: We consider the new divisor 334 and the new remainder 203, and apply the division lemma to get
334 = 203 x 1 + 131
We consider the new divisor 203 and the new remainder 131,and apply the division lemma to get
203 = 131 x 1 + 72
We consider the new divisor 131 and the new remainder 72,and apply the division lemma to get
131 = 72 x 1 + 59
We consider the new divisor 72 and the new remainder 59,and apply the division lemma to get
72 = 59 x 1 + 13
We consider the new divisor 59 and the new remainder 13,and apply the division lemma to get
59 = 13 x 4 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 871 and 537 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(59,13) = HCF(72,59) = HCF(131,72) = HCF(203,131) = HCF(334,203) = HCF(537,334) = HCF(871,537) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 1, we apply the division lemma to 680 and 1, to get
680 = 1 x 680 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 680 is 1
Notice that 1 = HCF(680,1) .
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Frequently Asked Questions on HCF of 871, 537, 680 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 871, 537, 680?
Answer: HCF of 871, 537, 680 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 871, 537, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 871, 537, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.