Highest Common Factor of 709, 643, 361 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 709, 643, 361 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 709, 643, 361 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 709, 643, 361 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 709, 643, 361 is 1.
HCF(709, 643, 361) = 1
HCF of 709, 643, 361 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 709, 643, 361 is 1.
Highest Common Factor of 709,643,361 is 1
Step 1: Since 709 > 643, we apply the division lemma to 709 and 643, to get
709 = 643 x 1 + 66
Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 66 and 643, to get
643 = 66 x 9 + 49
Step 3: We consider the new divisor 66 and the new remainder 49, and apply the division lemma to get
66 = 49 x 1 + 17
We consider the new divisor 49 and the new remainder 17,and apply the division lemma to get
49 = 17 x 2 + 15
We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get
17 = 15 x 1 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 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 709 and 643 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(49,17) = HCF(66,49) = HCF(643,66) = HCF(709,643) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 361 > 1, we apply the division lemma to 361 and 1, to get
361 = 1 x 361 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 361 is 1
Notice that 1 = HCF(361,1) .
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Frequently Asked Questions on HCF of 709, 643, 361 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 709, 643, 361?
Answer: HCF of 709, 643, 361 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 709, 643, 361 using Euclid's Algorithm?
Answer: For arbitrary numbers 709, 643, 361 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.