Highest Common Factor of 557, 344, 411 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 557, 344, 411 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 557, 344, 411 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 557, 344, 411 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 557, 344, 411 is 1.
HCF(557, 344, 411) = 1
HCF of 557, 344, 411 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 557, 344, 411 is 1.
Highest Common Factor of 557,344,411 is 1
Step 1: Since 557 > 344, we apply the division lemma to 557 and 344, to get
557 = 344 x 1 + 213
Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 213 and 344, to get
344 = 213 x 1 + 131
Step 3: We consider the new divisor 213 and the new remainder 131, and apply the division lemma to get
213 = 131 x 1 + 82
We consider the new divisor 131 and the new remainder 82,and apply the division lemma to get
131 = 82 x 1 + 49
We consider the new divisor 82 and the new remainder 49,and apply the division lemma to get
82 = 49 x 1 + 33
We consider the new divisor 49 and the new remainder 33,and apply the division lemma to get
49 = 33 x 1 + 16
We consider the new divisor 33 and the new remainder 16,and apply the division lemma to get
33 = 16 x 2 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 557 and 344 is 1
Notice that 1 = HCF(16,1) = HCF(33,16) = HCF(49,33) = HCF(82,49) = HCF(131,82) = HCF(213,131) = HCF(344,213) = HCF(557,344) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 411 > 1, we apply the division lemma to 411 and 1, to get
411 = 1 x 411 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 411 is 1
Notice that 1 = HCF(411,1) .
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Frequently Asked Questions on HCF of 557, 344, 411 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 557, 344, 411?
Answer: HCF of 557, 344, 411 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 557, 344, 411 using Euclid's Algorithm?
Answer: For arbitrary numbers 557, 344, 411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.