Highest Common Factor of 711, 274, 129 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 711, 274, 129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 711, 274, 129 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 711, 274, 129 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 711, 274, 129 is 1.
HCF(711, 274, 129) = 1
HCF of 711, 274, 129 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 711, 274, 129 is 1.
Highest Common Factor of 711,274,129 is 1
Step 1: Since 711 > 274, we apply the division lemma to 711 and 274, to get
711 = 274 x 2 + 163
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 163 and 274, to get
274 = 163 x 1 + 111
Step 3: We consider the new divisor 163 and the new remainder 111, and apply the division lemma to get
163 = 111 x 1 + 52
We consider the new divisor 111 and the new remainder 52,and apply the division lemma to get
111 = 52 x 2 + 7
We consider the new divisor 52 and the new remainder 7,and apply the division lemma to get
52 = 7 x 7 + 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 711 and 274 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(52,7) = HCF(111,52) = HCF(163,111) = HCF(274,163) = HCF(711,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 129 > 1, we apply the division lemma to 129 and 1, to get
129 = 1 x 129 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 129 is 1
Notice that 1 = HCF(129,1) .
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Frequently Asked Questions on HCF of 711, 274, 129 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 711, 274, 129?
Answer: HCF of 711, 274, 129 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 711, 274, 129 using Euclid's Algorithm?
Answer: For arbitrary numbers 711, 274, 129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.