Highest Common Factor of 866, 680, 534 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 866, 680, 534 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 866, 680, 534 is 2 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 866, 680, 534 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 866, 680, 534 is 2.
HCF(866, 680, 534) = 2
HCF of 866, 680, 534 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 866, 680, 534 is 2.
Highest Common Factor of 866,680,534 is 2
Step 1: Since 866 > 680, we apply the division lemma to 866 and 680, to get
866 = 680 x 1 + 186
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 186 and 680, to get
680 = 186 x 3 + 122
Step 3: We consider the new divisor 186 and the new remainder 122, and apply the division lemma to get
186 = 122 x 1 + 64
We consider the new divisor 122 and the new remainder 64,and apply the division lemma to get
122 = 64 x 1 + 58
We consider the new divisor 64 and the new remainder 58,and apply the division lemma to get
64 = 58 x 1 + 6
We consider the new divisor 58 and the new remainder 6,and apply the division lemma to get
58 = 6 x 9 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 866 and 680 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(58,6) = HCF(64,58) = HCF(122,64) = HCF(186,122) = HCF(680,186) = HCF(866,680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 534 > 2, we apply the division lemma to 534 and 2, to get
534 = 2 x 267 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 534 is 2
Notice that 2 = HCF(534,2) .
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Frequently Asked Questions on HCF of 866, 680, 534 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 866, 680, 534?
Answer: HCF of 866, 680, 534 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 866, 680, 534 using Euclid's Algorithm?
Answer: For arbitrary numbers 866, 680, 534 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.