Highest Common Factor of 677, 588, 549 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 677, 588, 549 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 677, 588, 549 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 677, 588, 549 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 677, 588, 549 is 1.
HCF(677, 588, 549) = 1
HCF of 677, 588, 549 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 677, 588, 549 is 1.
Highest Common Factor of 677,588,549 is 1
Step 1: Since 677 > 588, we apply the division lemma to 677 and 588, to get
677 = 588 x 1 + 89
Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 89 and 588, to get
588 = 89 x 6 + 54
Step 3: We consider the new divisor 89 and the new remainder 54, and apply the division lemma to get
89 = 54 x 1 + 35
We consider the new divisor 54 and the new remainder 35,and apply the division lemma to get
54 = 35 x 1 + 19
We consider the new divisor 35 and the new remainder 19,and apply the division lemma to get
35 = 19 x 1 + 16
We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get
19 = 16 x 1 + 3
We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get
16 = 3 x 5 + 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 677 and 588 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(35,19) = HCF(54,35) = HCF(89,54) = HCF(588,89) = HCF(677,588) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 549 > 1, we apply the division lemma to 549 and 1, to get
549 = 1 x 549 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 549 is 1
Notice that 1 = HCF(549,1) .
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Frequently Asked Questions on HCF of 677, 588, 549 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 677, 588, 549?
Answer: HCF of 677, 588, 549 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 677, 588, 549 using Euclid's Algorithm?
Answer: For arbitrary numbers 677, 588, 549 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.