Highest Common Factor of 729, 7802, 3271 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, 7802, 3271 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 7802, 3271 is 1 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, 7802, 3271 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, 7802, 3271 is 1.
HCF(729, 7802, 3271) = 1
HCF of 729, 7802, 3271 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, 7802, 3271 is 1.
Highest Common Factor of 729,7802,3271 is 1
Step 1: Since 7802 > 729, we apply the division lemma to 7802 and 729, to get
7802 = 729 x 10 + 512
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 512 and 729, to get
729 = 512 x 1 + 217
Step 3: We consider the new divisor 512 and the new remainder 217, and apply the division lemma to get
512 = 217 x 2 + 78
We consider the new divisor 217 and the new remainder 78,and apply the division lemma to get
217 = 78 x 2 + 61
We consider the new divisor 78 and the new remainder 61,and apply the division lemma to get
78 = 61 x 1 + 17
We consider the new divisor 61 and the new remainder 17,and apply the division lemma to get
61 = 17 x 3 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 729 and 7802 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(61,17) = HCF(78,61) = HCF(217,78) = HCF(512,217) = HCF(729,512) = HCF(7802,729) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3271 > 1, we apply the division lemma to 3271 and 1, to get
3271 = 1 x 3271 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3271 is 1
Notice that 1 = HCF(3271,1) .
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Frequently Asked Questions on HCF of 729, 7802, 3271 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, 7802, 3271?
Answer: HCF of 729, 7802, 3271 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 7802, 3271 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 7802, 3271 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.