Highest Common Factor of 678, 772, 727 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, 772, 727 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 772, 727 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, 772, 727 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, 772, 727 is 1.
HCF(678, 772, 727) = 1
HCF of 678, 772, 727 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, 772, 727 is 1.
Highest Common Factor of 678,772,727 is 1
Step 1: Since 772 > 678, we apply the division lemma to 772 and 678, to get
772 = 678 x 1 + 94
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 94 and 678, to get
678 = 94 x 7 + 20
Step 3: We consider the new divisor 94 and the new remainder 20, and apply the division lemma to get
94 = 20 x 4 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 772 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(94,20) = HCF(678,94) = HCF(772,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 727 > 2, we apply the division lemma to 727 and 2, to get
727 = 2 x 363 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 727 is 1
Notice that 1 = HCF(2,1) = HCF(727,2) .
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Frequently Asked Questions on HCF of 678, 772, 727 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, 772, 727?
Answer: HCF of 678, 772, 727 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 772, 727 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 772, 727 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.