Highest Common Factor of 677, 819, 54 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 677, 819, 54 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 677, 819, 54 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 677, 819, 54 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 677, 819, 54 is 1.
HCF(677, 819, 54) = 1
HCF of 677, 819, 54 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 677, 819, 54 is 1.
Highest Common Factor of 677,819,54 is 1
Step 1: Since 819 > 677, we apply the division lemma to 819 and 677, to get
819 = 677 x 1 + 142
Step 2: Since the reminder 677 ≠ 0, we apply division lemma to 142 and 677, to get
677 = 142 x 4 + 109
Step 3: We consider the new divisor 142 and the new remainder 109, and apply the division lemma to get
142 = 109 x 1 + 33
We consider the new divisor 109 and the new remainder 33,and apply the division lemma to get
109 = 33 x 3 + 10
We consider the new divisor 33 and the new remainder 10,and apply the division lemma to get
33 = 10 x 3 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 677 and 819 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(33,10) = HCF(109,33) = HCF(142,109) = HCF(677,142) = HCF(819,677) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 1, we apply the division lemma to 54 and 1, to get
54 = 1 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 54 is 1
Notice that 1 = HCF(54,1) .
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Frequently Asked Questions on HCF of 677, 819, 54 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 677, 819, 54?
Answer: HCF of 677, 819, 54 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 677, 819, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 677, 819, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.