Highest Common Factor of 471, 648, 64 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 471, 648, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 471, 648, 64 is 1 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 471, 648, 64 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 471, 648, 64 is 1.
HCF(471, 648, 64) = 1
HCF of 471, 648, 64 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 471, 648, 64 is 1.
Highest Common Factor of 471,648,64 is 1
Step 1: Since 648 > 471, we apply the division lemma to 648 and 471, to get
648 = 471 x 1 + 177
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 177 and 471, to get
471 = 177 x 2 + 117
Step 3: We consider the new divisor 177 and the new remainder 117, and apply the division lemma to get
177 = 117 x 1 + 60
We consider the new divisor 117 and the new remainder 60,and apply the division lemma to get
117 = 60 x 1 + 57
We consider the new divisor 60 and the new remainder 57,and apply the division lemma to get
60 = 57 x 1 + 3
We consider the new divisor 57 and the new remainder 3,and apply the division lemma to get
57 = 3 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 471 and 648 is 3
Notice that 3 = HCF(57,3) = HCF(60,57) = HCF(117,60) = HCF(177,117) = HCF(471,177) = HCF(648,471) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 64 > 3, we apply the division lemma to 64 and 3, to get
64 = 3 x 21 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 64 is 1
Notice that 1 = HCF(3,1) = HCF(64,3) .
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Frequently Asked Questions on HCF of 471, 648, 64 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 471, 648, 64?
Answer: HCF of 471, 648, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 471, 648, 64 using Euclid's Algorithm?
Answer: For arbitrary numbers 471, 648, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
