Highest Common Factor of 729, 8619, 2982 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 729, 8619, 2982 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 8619, 2982 is 3 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 729, 8619, 2982 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 729, 8619, 2982 is 3.
HCF(729, 8619, 2982) = 3
HCF of 729, 8619, 2982 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 729, 8619, 2982 is 3.
Highest Common Factor of 729,8619,2982 is 3
Step 1: Since 8619 > 729, we apply the division lemma to 8619 and 729, to get
8619 = 729 x 11 + 600
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 600 and 729, to get
729 = 600 x 1 + 129
Step 3: We consider the new divisor 600 and the new remainder 129, and apply the division lemma to get
600 = 129 x 4 + 84
We consider the new divisor 129 and the new remainder 84,and apply the division lemma to get
129 = 84 x 1 + 45
We consider the new divisor 84 and the new remainder 45,and apply the division lemma to get
84 = 45 x 1 + 39
We consider the new divisor 45 and the new remainder 39,and apply the division lemma to get
45 = 39 x 1 + 6
We consider the new divisor 39 and the new remainder 6,and apply the division lemma to get
39 = 6 x 6 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 729 and 8619 is 3
Notice that 3 = HCF(6,3) = HCF(39,6) = HCF(45,39) = HCF(84,45) = HCF(129,84) = HCF(600,129) = HCF(729,600) = HCF(8619,729) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2982 > 3, we apply the division lemma to 2982 and 3, to get
2982 = 3 x 994 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 2982 is 3
Notice that 3 = HCF(2982,3) .
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Frequently Asked Questions on HCF of 729, 8619, 2982 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 729, 8619, 2982?
Answer: HCF of 729, 8619, 2982 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 8619, 2982 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 8619, 2982 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.