Highest Common Factor of 617, 861, 728 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 617, 861, 728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 617, 861, 728 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 617, 861, 728 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 617, 861, 728 is 1.
HCF(617, 861, 728) = 1
HCF of 617, 861, 728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 617, 861, 728 is 1.
Highest Common Factor of 617,861,728 is 1
Step 1: Since 861 > 617, we apply the division lemma to 861 and 617, to get
861 = 617 x 1 + 244
Step 2: Since the reminder 617 ≠ 0, we apply division lemma to 244 and 617, to get
617 = 244 x 2 + 129
Step 3: We consider the new divisor 244 and the new remainder 129, and apply the division lemma to get
244 = 129 x 1 + 115
We consider the new divisor 129 and the new remainder 115,and apply the division lemma to get
129 = 115 x 1 + 14
We consider the new divisor 115 and the new remainder 14,and apply the division lemma to get
115 = 14 x 8 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 617 and 861 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(115,14) = HCF(129,115) = HCF(244,129) = HCF(617,244) = HCF(861,617) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 728 > 1, we apply the division lemma to 728 and 1, to get
728 = 1 x 728 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 728 is 1
Notice that 1 = HCF(728,1) .
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Frequently Asked Questions on HCF of 617, 861, 728 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 617, 861, 728?
Answer: HCF of 617, 861, 728 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 617, 861, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 617, 861, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
