Highest Common Factor of 678, 477, 116 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, 477, 116 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 477, 116 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 678, 477, 116 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, 477, 116 is 1.
HCF(678, 477, 116) = 1
HCF of 678, 477, 116 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, 477, 116 is 1.
Highest Common Factor of 678,477,116 is 1
Step 1: Since 678 > 477, we apply the division lemma to 678 and 477, to get
678 = 477 x 1 + 201
Step 2: Since the reminder 477 ≠ 0, we apply division lemma to 201 and 477, to get
477 = 201 x 2 + 75
Step 3: We consider the new divisor 201 and the new remainder 75, and apply the division lemma to get
201 = 75 x 2 + 51
We consider the new divisor 75 and the new remainder 51,and apply the division lemma to get
75 = 51 x 1 + 24
We consider the new divisor 51 and the new remainder 24,and apply the division lemma to get
51 = 24 x 2 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 678 and 477 is 3
Notice that 3 = HCF(24,3) = HCF(51,24) = HCF(75,51) = HCF(201,75) = HCF(477,201) = HCF(678,477) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 3, we apply the division lemma to 116 and 3, to get
116 = 3 x 38 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 116 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(116,3) .
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Frequently Asked Questions on HCF of 678, 477, 116 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, 477, 116?
Answer: HCF of 678, 477, 116 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 477, 116 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 477, 116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.