Highest Common Factor of 812, 580, 866 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 812, 580, 866 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 580, 866 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 812, 580, 866 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 812, 580, 866 is 2.
HCF(812, 580, 866) = 2
HCF of 812, 580, 866 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 580, 866 is 2.
Highest Common Factor of 812,580,866 is 2
Step 1: Since 812 > 580, we apply the division lemma to 812 and 580, to get
812 = 580 x 1 + 232
Step 2: Since the reminder 580 ≠ 0, we apply division lemma to 232 and 580, to get
580 = 232 x 2 + 116
Step 3: We consider the new divisor 232 and the new remainder 116, and apply the division lemma to get
232 = 116 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 116, the HCF of 812 and 580 is 116
Notice that 116 = HCF(232,116) = HCF(580,232) = HCF(812,580) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 866 > 116, we apply the division lemma to 866 and 116, to get
866 = 116 x 7 + 54
Step 2: Since the reminder 116 ≠ 0, we apply division lemma to 54 and 116, to get
116 = 54 x 2 + 8
Step 3: We consider the new divisor 54 and the new remainder 8, and apply the division lemma to get
54 = 8 x 6 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 116 and 866 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(54,8) = HCF(116,54) = HCF(866,116) .
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Frequently Asked Questions on HCF of 812, 580, 866 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 812, 580, 866?
Answer: HCF of 812, 580, 866 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 580, 866 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 580, 866 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.