Highest Common Factor of 521, 612, 644 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 521, 612, 644 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 521, 612, 644 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 521, 612, 644 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 521, 612, 644 is 1.
HCF(521, 612, 644) = 1
HCF of 521, 612, 644 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 521, 612, 644 is 1.
Highest Common Factor of 521,612,644 is 1
Step 1: Since 612 > 521, we apply the division lemma to 612 and 521, to get
612 = 521 x 1 + 91
Step 2: Since the reminder 521 ≠ 0, we apply division lemma to 91 and 521, to get
521 = 91 x 5 + 66
Step 3: We consider the new divisor 91 and the new remainder 66, and apply the division lemma to get
91 = 66 x 1 + 25
We consider the new divisor 66 and the new remainder 25,and apply the division lemma to get
66 = 25 x 2 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 521 and 612 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(66,25) = HCF(91,66) = HCF(521,91) = HCF(612,521) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 644 > 1, we apply the division lemma to 644 and 1, to get
644 = 1 x 644 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 644 is 1
Notice that 1 = HCF(644,1) .
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Frequently Asked Questions on HCF of 521, 612, 644 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 521, 612, 644?
Answer: HCF of 521, 612, 644 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 521, 612, 644 using Euclid's Algorithm?
Answer: For arbitrary numbers 521, 612, 644 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
