Highest Common Factor of 660, 231, 486 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 660, 231, 486 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 231, 486 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 660, 231, 486 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 660, 231, 486 is 3.
HCF(660, 231, 486) = 3
HCF of 660, 231, 486 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 231, 486 is 3.
Highest Common Factor of 660,231,486 is 3
Step 1: Since 660 > 231, we apply the division lemma to 660 and 231, to get
660 = 231 x 2 + 198
Step 2: Since the reminder 231 ≠ 0, we apply division lemma to 198 and 231, to get
231 = 198 x 1 + 33
Step 3: We consider the new divisor 198 and the new remainder 33, and apply the division lemma to get
198 = 33 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 33, the HCF of 660 and 231 is 33
Notice that 33 = HCF(198,33) = HCF(231,198) = HCF(660,231) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 486 > 33, we apply the division lemma to 486 and 33, to get
486 = 33 x 14 + 24
Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 24 and 33, to get
33 = 24 x 1 + 9
Step 3: We consider the new divisor 24 and the new remainder 9, and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 33 and 486 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(486,33) .
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Frequently Asked Questions on HCF of 660, 231, 486 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 660, 231, 486?
Answer: HCF of 660, 231, 486 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 231, 486 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 231, 486 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.