Highest Common Factor of 654, 378, 71 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 654, 378, 71 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 378, 71 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 654, 378, 71 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 654, 378, 71 is 1.
HCF(654, 378, 71) = 1
HCF of 654, 378, 71 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 654, 378, 71 is 1.
Highest Common Factor of 654,378,71 is 1
Step 1: Since 654 > 378, we apply the division lemma to 654 and 378, to get
654 = 378 x 1 + 276
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 276 and 378, to get
378 = 276 x 1 + 102
Step 3: We consider the new divisor 276 and the new remainder 102, and apply the division lemma to get
276 = 102 x 2 + 72
We consider the new divisor 102 and the new remainder 72,and apply the division lemma to get
102 = 72 x 1 + 30
We consider the new divisor 72 and the new remainder 30,and apply the division lemma to get
72 = 30 x 2 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 654 and 378 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(72,30) = HCF(102,72) = HCF(276,102) = HCF(378,276) = HCF(654,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 71 > 6, we apply the division lemma to 71 and 6, to get
71 = 6 x 11 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 71 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(71,6) .
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Frequently Asked Questions on HCF of 654, 378, 71 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 654, 378, 71?
Answer: HCF of 654, 378, 71 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 378, 71 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 378, 71 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.