Highest Common Factor of 549, 613, 51 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 549, 613, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 549, 613, 51 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 549, 613, 51 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 549, 613, 51 is 1.
HCF(549, 613, 51) = 1
HCF of 549, 613, 51 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 549, 613, 51 is 1.
Highest Common Factor of 549,613,51 is 1
Step 1: Since 613 > 549, we apply the division lemma to 613 and 549, to get
613 = 549 x 1 + 64
Step 2: Since the reminder 549 ≠ 0, we apply division lemma to 64 and 549, to get
549 = 64 x 8 + 37
Step 3: We consider the new divisor 64 and the new remainder 37, and apply the division lemma to get
64 = 37 x 1 + 27
We consider the new divisor 37 and the new remainder 27,and apply the division lemma to get
37 = 27 x 1 + 10
We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get
27 = 10 x 2 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 549 and 613 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(37,27) = HCF(64,37) = HCF(549,64) = HCF(613,549) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 1, we apply the division lemma to 51 and 1, to get
51 = 1 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51 is 1
Notice that 1 = HCF(51,1) .
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Frequently Asked Questions on HCF of 549, 613, 51 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 549, 613, 51?
Answer: HCF of 549, 613, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 549, 613, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 549, 613, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.