Highest Common Factor of 678, 2012 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 678, 2012 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 2012 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 678, 2012 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 678, 2012 is 2.
HCF(678, 2012) = 2
HCF of 678, 2012 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 2012 is 2.
Highest Common Factor of 678,2012 is 2
Step 1: Since 2012 > 678, we apply the division lemma to 2012 and 678, to get
2012 = 678 x 2 + 656
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 656 and 678, to get
678 = 656 x 1 + 22
Step 3: We consider the new divisor 656 and the new remainder 22, and apply the division lemma to get
656 = 22 x 29 + 18
We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get
22 = 18 x 1 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 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 678 and 2012 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(656,22) = HCF(678,656) = HCF(2012,678) .
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Frequently Asked Questions on HCF of 678, 2012 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 678, 2012?
Answer: HCF of 678, 2012 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 2012 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 2012 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.