Highest Common Factor of 696, 971, 614 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 696, 971, 614 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 696, 971, 614 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 696, 971, 614 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 696, 971, 614 is 1.
HCF(696, 971, 614) = 1
HCF of 696, 971, 614 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 696, 971, 614 is 1.
Highest Common Factor of 696,971,614 is 1
Step 1: Since 971 > 696, we apply the division lemma to 971 and 696, to get
971 = 696 x 1 + 275
Step 2: Since the reminder 696 ≠ 0, we apply division lemma to 275 and 696, to get
696 = 275 x 2 + 146
Step 3: We consider the new divisor 275 and the new remainder 146, and apply the division lemma to get
275 = 146 x 1 + 129
We consider the new divisor 146 and the new remainder 129,and apply the division lemma to get
146 = 129 x 1 + 17
We consider the new divisor 129 and the new remainder 17,and apply the division lemma to get
129 = 17 x 7 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 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 696 and 971 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(129,17) = HCF(146,129) = HCF(275,146) = HCF(696,275) = HCF(971,696) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 614 > 1, we apply the division lemma to 614 and 1, to get
614 = 1 x 614 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 614 is 1
Notice that 1 = HCF(614,1) .
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Frequently Asked Questions on HCF of 696, 971, 614 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 696, 971, 614?
Answer: HCF of 696, 971, 614 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 696, 971, 614 using Euclid's Algorithm?
Answer: For arbitrary numbers 696, 971, 614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.