Highest Common Factor of 820, 610, 612 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 820, 610, 612 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 820, 610, 612 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 820, 610, 612 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 820, 610, 612 is 2.
HCF(820, 610, 612) = 2
HCF of 820, 610, 612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 820, 610, 612 is 2.
Highest Common Factor of 820,610,612 is 2
Step 1: Since 820 > 610, we apply the division lemma to 820 and 610, to get
820 = 610 x 1 + 210
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 210 and 610, to get
610 = 210 x 2 + 190
Step 3: We consider the new divisor 210 and the new remainder 190, and apply the division lemma to get
210 = 190 x 1 + 20
We consider the new divisor 190 and the new remainder 20,and apply the division lemma to get
190 = 20 x 9 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 820 and 610 is 10
Notice that 10 = HCF(20,10) = HCF(190,20) = HCF(210,190) = HCF(610,210) = HCF(820,610) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 612 > 10, we apply the division lemma to 612 and 10, to get
612 = 10 x 61 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 612 is 2
Notice that 2 = HCF(10,2) = HCF(612,10) .
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Frequently Asked Questions on HCF of 820, 610, 612 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 820, 610, 612?
Answer: HCF of 820, 610, 612 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 820, 610, 612 using Euclid's Algorithm?
Answer: For arbitrary numbers 820, 610, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.