Highest Common Factor of 678, 963, 777 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, 963, 777 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 963, 777 is 3 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, 963, 777 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, 963, 777 is 3.
HCF(678, 963, 777) = 3
HCF of 678, 963, 777 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, 963, 777 is 3.
Highest Common Factor of 678,963,777 is 3
Step 1: Since 963 > 678, we apply the division lemma to 963 and 678, to get
963 = 678 x 1 + 285
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 285 and 678, to get
678 = 285 x 2 + 108
Step 3: We consider the new divisor 285 and the new remainder 108, and apply the division lemma to get
285 = 108 x 2 + 69
We consider the new divisor 108 and the new remainder 69,and apply the division lemma to get
108 = 69 x 1 + 39
We consider the new divisor 69 and the new remainder 39,and apply the division lemma to get
69 = 39 x 1 + 30
We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get
39 = 30 x 1 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 678 and 963 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(69,39) = HCF(108,69) = HCF(285,108) = HCF(678,285) = HCF(963,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 777 > 3, we apply the division lemma to 777 and 3, to get
777 = 3 x 259 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 777 is 3
Notice that 3 = HCF(777,3) .
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Frequently Asked Questions on HCF of 678, 963, 777 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, 963, 777?
Answer: HCF of 678, 963, 777 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 963, 777 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 963, 777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.