Highest Common Factor of 882, 546, 820 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 882, 546, 820 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 882, 546, 820 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 882, 546, 820 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 882, 546, 820 is 2.
HCF(882, 546, 820) = 2
HCF of 882, 546, 820 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 882, 546, 820 is 2.
Highest Common Factor of 882,546,820 is 2
Step 1: Since 882 > 546, we apply the division lemma to 882 and 546, to get
882 = 546 x 1 + 336
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 336 and 546, to get
546 = 336 x 1 + 210
Step 3: We consider the new divisor 336 and the new remainder 210, and apply the division lemma to get
336 = 210 x 1 + 126
We consider the new divisor 210 and the new remainder 126,and apply the division lemma to get
210 = 126 x 1 + 84
We consider the new divisor 126 and the new remainder 84,and apply the division lemma to get
126 = 84 x 1 + 42
We consider the new divisor 84 and the new remainder 42,and apply the division lemma to get
84 = 42 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 882 and 546 is 42
Notice that 42 = HCF(84,42) = HCF(126,84) = HCF(210,126) = HCF(336,210) = HCF(546,336) = HCF(882,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 820 > 42, we apply the division lemma to 820 and 42, to get
820 = 42 x 19 + 22
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 22 and 42, to get
42 = 22 x 1 + 20
Step 3: We consider the new divisor 22 and the new remainder 20, and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2, and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 42 and 820 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(820,42) .
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Frequently Asked Questions on HCF of 882, 546, 820 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 882, 546, 820?
Answer: HCF of 882, 546, 820 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 882, 546, 820 using Euclid's Algorithm?
Answer: For arbitrary numbers 882, 546, 820 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.