Highest Common Factor of 621, 678, 663 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 621, 678, 663 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 621, 678, 663 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 621, 678, 663 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 621, 678, 663 is 3.
HCF(621, 678, 663) = 3
HCF of 621, 678, 663 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 621, 678, 663 is 3.
Highest Common Factor of 621,678,663 is 3
Step 1: Since 678 > 621, we apply the division lemma to 678 and 621, to get
678 = 621 x 1 + 57
Step 2: Since the reminder 621 ≠ 0, we apply division lemma to 57 and 621, to get
621 = 57 x 10 + 51
Step 3: We consider the new divisor 57 and the new remainder 51, and apply the division lemma to get
57 = 51 x 1 + 6
We consider the new divisor 51 and the new remainder 6,and apply the division lemma to get
51 = 6 x 8 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 621 and 678 is 3
Notice that 3 = HCF(6,3) = HCF(51,6) = HCF(57,51) = HCF(621,57) = HCF(678,621) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 663 > 3, we apply the division lemma to 663 and 3, to get
663 = 3 x 221 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 663 is 3
Notice that 3 = HCF(663,3) .
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Frequently Asked Questions on HCF of 621, 678, 663 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 621, 678, 663?
Answer: HCF of 621, 678, 663 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 621, 678, 663 using Euclid's Algorithm?
Answer: For arbitrary numbers 621, 678, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.