Highest Common Factor of 820, 1704, 3146 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, 1704, 3146 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 820, 1704, 3146 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, 1704, 3146 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, 1704, 3146 is 2.
HCF(820, 1704, 3146) = 2
HCF of 820, 1704, 3146 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, 1704, 3146 is 2.
Highest Common Factor of 820,1704,3146 is 2
Step 1: Since 1704 > 820, we apply the division lemma to 1704 and 820, to get
1704 = 820 x 2 + 64
Step 2: Since the reminder 820 ≠ 0, we apply division lemma to 64 and 820, to get
820 = 64 x 12 + 52
Step 3: We consider the new divisor 64 and the new remainder 52, and apply the division lemma to get
64 = 52 x 1 + 12
We consider the new divisor 52 and the new remainder 12,and apply the division lemma to get
52 = 12 x 4 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 820 and 1704 is 4
Notice that 4 = HCF(12,4) = HCF(52,12) = HCF(64,52) = HCF(820,64) = HCF(1704,820) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3146 > 4, we apply the division lemma to 3146 and 4, to get
3146 = 4 x 786 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 3146 is 2
Notice that 2 = HCF(4,2) = HCF(3146,4) .
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Frequently Asked Questions on HCF of 820, 1704, 3146 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, 1704, 3146?
Answer: HCF of 820, 1704, 3146 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 820, 1704, 3146 using Euclid's Algorithm?
Answer: For arbitrary numbers 820, 1704, 3146 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.