Highest Common Factor of 666, 852, 621 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 666, 852, 621 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 666, 852, 621 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 666, 852, 621 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 666, 852, 621 is 3.
HCF(666, 852, 621) = 3
HCF of 666, 852, 621 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 666, 852, 621 is 3.
Highest Common Factor of 666,852,621 is 3
Step 1: Since 852 > 666, we apply the division lemma to 852 and 666, to get
852 = 666 x 1 + 186
Step 2: Since the reminder 666 ≠ 0, we apply division lemma to 186 and 666, to get
666 = 186 x 3 + 108
Step 3: We consider the new divisor 186 and the new remainder 108, and apply the division lemma to get
186 = 108 x 1 + 78
We consider the new divisor 108 and the new remainder 78,and apply the division lemma to get
108 = 78 x 1 + 30
We consider the new divisor 78 and the new remainder 30,and apply the division lemma to get
78 = 30 x 2 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 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 666 and 852 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(78,30) = HCF(108,78) = HCF(186,108) = HCF(666,186) = HCF(852,666) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 621 > 6, we apply the division lemma to 621 and 6, to get
621 = 6 x 103 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, 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 6 and 621 is 3
Notice that 3 = HCF(6,3) = HCF(621,6) .
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Frequently Asked Questions on HCF of 666, 852, 621 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 666, 852, 621?
Answer: HCF of 666, 852, 621 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 666, 852, 621 using Euclid's Algorithm?
Answer: For arbitrary numbers 666, 852, 621 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.