Highest Common Factor of 786, 171, 12 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 786, 171, 12 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 786, 171, 12 is 3 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 786, 171, 12 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 786, 171, 12 is 3.
HCF(786, 171, 12) = 3
HCF of 786, 171, 12 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 786, 171, 12 is 3.
Highest Common Factor of 786,171,12 is 3
Step 1: Since 786 > 171, we apply the division lemma to 786 and 171, to get
786 = 171 x 4 + 102
Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 102 and 171, to get
171 = 102 x 1 + 69
Step 3: We consider the new divisor 102 and the new remainder 69, and apply the division lemma to get
102 = 69 x 1 + 33
We consider the new divisor 69 and the new remainder 33,and apply the division lemma to get
69 = 33 x 2 + 3
We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 786 and 171 is 3
Notice that 3 = HCF(33,3) = HCF(69,33) = HCF(102,69) = HCF(171,102) = HCF(786,171) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12 > 3, we apply the division lemma to 12 and 3, to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 12 is 3
Notice that 3 = HCF(12,3) .
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Frequently Asked Questions on HCF of 786, 171, 12 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 786, 171, 12?
Answer: HCF of 786, 171, 12 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 786, 171, 12 using Euclid's Algorithm?
Answer: For arbitrary numbers 786, 171, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.