Highest Common Factor of 736, 206, 71 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 736, 206, 71 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 736, 206, 71 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 736, 206, 71 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 736, 206, 71 is 1.
HCF(736, 206, 71) = 1
HCF of 736, 206, 71 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 736, 206, 71 is 1.
Highest Common Factor of 736,206,71 is 1
Step 1: Since 736 > 206, we apply the division lemma to 736 and 206, to get
736 = 206 x 3 + 118
Step 2: Since the reminder 206 ≠ 0, we apply division lemma to 118 and 206, to get
206 = 118 x 1 + 88
Step 3: We consider the new divisor 118 and the new remainder 88, and apply the division lemma to get
118 = 88 x 1 + 30
We consider the new divisor 88 and the new remainder 30,and apply the division lemma to get
88 = 30 x 2 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 736 and 206 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(88,30) = HCF(118,88) = HCF(206,118) = HCF(736,206) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 71 > 2, we apply the division lemma to 71 and 2, to get
71 = 2 x 35 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 71 is 1
Notice that 1 = HCF(2,1) = HCF(71,2) .
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Frequently Asked Questions on HCF of 736, 206, 71 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 736, 206, 71?
Answer: HCF of 736, 206, 71 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 736, 206, 71 using Euclid's Algorithm?
Answer: For arbitrary numbers 736, 206, 71 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.