Highest Common Factor of 453, 624, 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 453, 624, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 453, 624, 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 453, 624, 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 453, 624, 64 is 1.
HCF(453, 624, 64) = 1
HCF of 453, 624, 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 453, 624, 64 is 1.
Highest Common Factor of 453,624,64 is 1
Step 1: Since 624 > 453, we apply the division lemma to 624 and 453, to get
624 = 453 x 1 + 171
Step 2: Since the reminder 453 ≠ 0, we apply division lemma to 171 and 453, to get
453 = 171 x 2 + 111
Step 3: We consider the new divisor 171 and the new remainder 111, and apply the division lemma to get
171 = 111 x 1 + 60
We consider the new divisor 111 and the new remainder 60,and apply the division lemma to get
111 = 60 x 1 + 51
We consider the new divisor 60 and the new remainder 51,and apply the division lemma to get
60 = 51 x 1 + 9
We consider the new divisor 51 and the new remainder 9,and apply the division lemma to get
51 = 9 x 5 + 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 453 and 624 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(51,9) = HCF(60,51) = HCF(111,60) = HCF(171,111) = HCF(453,171) = HCF(624,453) .
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 453, 624, 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 453, 624, 64?
Answer: HCF of 453, 624, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 453, 624, 64 using Euclid's Algorithm?
Answer: For arbitrary numbers 453, 624, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.