Highest Common Factor of 512, 786, 422 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 512, 786, 422 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 512, 786, 422 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 512, 786, 422 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 512, 786, 422 is 2.
HCF(512, 786, 422) = 2
HCF of 512, 786, 422 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 512, 786, 422 is 2.
Highest Common Factor of 512,786,422 is 2
Step 1: Since 786 > 512, we apply the division lemma to 786 and 512, to get
786 = 512 x 1 + 274
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 274 and 512, to get
512 = 274 x 1 + 238
Step 3: We consider the new divisor 274 and the new remainder 238, and apply the division lemma to get
274 = 238 x 1 + 36
We consider the new divisor 238 and the new remainder 36,and apply the division lemma to get
238 = 36 x 6 + 22
We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get
36 = 22 x 1 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 512 and 786 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(238,36) = HCF(274,238) = HCF(512,274) = HCF(786,512) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 422 > 2, we apply the division lemma to 422 and 2, to get
422 = 2 x 211 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 422 is 2
Notice that 2 = HCF(422,2) .
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Frequently Asked Questions on HCF of 512, 786, 422 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 512, 786, 422?
Answer: HCF of 512, 786, 422 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 512, 786, 422 using Euclid's Algorithm?
Answer: For arbitrary numbers 512, 786, 422 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.