Highest Common Factor of 660, 477, 648 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, 477, 648 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 477, 648 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, 477, 648 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, 477, 648 is 3.
HCF(660, 477, 648) = 3
HCF of 660, 477, 648 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, 477, 648 is 3.
Highest Common Factor of 660,477,648 is 3
Step 1: Since 660 > 477, we apply the division lemma to 660 and 477, to get
660 = 477 x 1 + 183
Step 2: Since the reminder 477 ≠ 0, we apply division lemma to 183 and 477, to get
477 = 183 x 2 + 111
Step 3: We consider the new divisor 183 and the new remainder 111, and apply the division lemma to get
183 = 111 x 1 + 72
We consider the new divisor 111 and the new remainder 72,and apply the division lemma to get
111 = 72 x 1 + 39
We consider the new divisor 72 and the new remainder 39,and apply the division lemma to get
72 = 39 x 1 + 33
We consider the new divisor 39 and the new remainder 33,and apply the division lemma to get
39 = 33 x 1 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 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 660 and 477 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(72,39) = HCF(111,72) = HCF(183,111) = HCF(477,183) = HCF(660,477) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 648 > 3, we apply the division lemma to 648 and 3, to get
648 = 3 x 216 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 648 is 3
Notice that 3 = HCF(648,3) .
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Frequently Asked Questions on HCF of 660, 477, 648 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, 477, 648?
Answer: HCF of 660, 477, 648 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 477, 648 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 477, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.