Highest Common Factor of 666, 617 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 666, 617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 666, 617 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 666, 617 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 666, 617 is 1.
HCF(666, 617) = 1
HCF of 666, 617 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 666, 617 is 1.
Highest Common Factor of 666,617 is 1
Step 1: Since 666 > 617, we apply the division lemma to 666 and 617, to get
666 = 617 x 1 + 49
Step 2: Since the reminder 617 ≠ 0, we apply division lemma to 49 and 617, to get
617 = 49 x 12 + 29
Step 3: We consider the new divisor 49 and the new remainder 29, and apply the division lemma to get
49 = 29 x 1 + 20
We consider the new divisor 29 and the new remainder 20,and apply the division lemma to get
29 = 20 x 1 + 9
We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get
20 = 9 x 2 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 666 and 617 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(29,20) = HCF(49,29) = HCF(617,49) = HCF(666,617) .
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Frequently Asked Questions on HCF of 666, 617 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 666, 617?
Answer: HCF of 666, 617 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 666, 617 using Euclid's Algorithm?
Answer: For arbitrary numbers 666, 617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.