Highest Common Factor of 680, 612, 806 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 680, 612, 806 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 612, 806 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 680, 612, 806 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 680, 612, 806 is 2.
HCF(680, 612, 806) = 2
HCF of 680, 612, 806 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 612, 806 is 2.
Highest Common Factor of 680,612,806 is 2
Step 1: Since 680 > 612, we apply the division lemma to 680 and 612, to get
680 = 612 x 1 + 68
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 68 and 612, to get
612 = 68 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 68, the HCF of 680 and 612 is 68
Notice that 68 = HCF(612,68) = HCF(680,612) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 806 > 68, we apply the division lemma to 806 and 68, to get
806 = 68 x 11 + 58
Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 58 and 68, to get
68 = 58 x 1 + 10
Step 3: We consider the new divisor 58 and the new remainder 10, and apply the division lemma to get
58 = 10 x 5 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 68 and 806 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(58,10) = HCF(68,58) = HCF(806,68) .
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Frequently Asked Questions on HCF of 680, 612, 806 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 680, 612, 806?
Answer: HCF of 680, 612, 806 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 612, 806 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 612, 806 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.