Highest Common Factor of 812, 126, 696 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 812, 126, 696 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 126, 696 is 2 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 812, 126, 696 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 812, 126, 696 is 2.
HCF(812, 126, 696) = 2
HCF of 812, 126, 696 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 126, 696 is 2.
Highest Common Factor of 812,126,696 is 2
Step 1: Since 812 > 126, we apply the division lemma to 812 and 126, to get
812 = 126 x 6 + 56
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 56 and 126, to get
126 = 56 x 2 + 14
Step 3: We consider the new divisor 56 and the new remainder 14, and apply the division lemma to get
56 = 14 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 812 and 126 is 14
Notice that 14 = HCF(56,14) = HCF(126,56) = HCF(812,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 696 > 14, we apply the division lemma to 696 and 14, to get
696 = 14 x 49 + 10
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 10 and 14, to get
14 = 10 x 1 + 4
Step 3: We consider the new divisor 10 and the new remainder 4, and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 696 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(696,14) .
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Frequently Asked Questions on HCF of 812, 126, 696 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 812, 126, 696?
Answer: HCF of 812, 126, 696 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 126, 696 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 126, 696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.