Highest Common Factor of 205, 557 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 205, 557 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 205, 557 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 205, 557 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 205, 557 is 1.
HCF(205, 557) = 1
HCF of 205, 557 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 205, 557 is 1.
Highest Common Factor of 205,557 is 1
Step 1: Since 557 > 205, we apply the division lemma to 557 and 205, to get
557 = 205 x 2 + 147
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 147 and 205, to get
205 = 147 x 1 + 58
Step 3: We consider the new divisor 147 and the new remainder 58, and apply the division lemma to get
147 = 58 x 2 + 31
We consider the new divisor 58 and the new remainder 31,and apply the division lemma to get
58 = 31 x 1 + 27
We consider the new divisor 31 and the new remainder 27,and apply the division lemma to get
31 = 27 x 1 + 4
We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get
27 = 4 x 6 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 205 and 557 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(31,27) = HCF(58,31) = HCF(147,58) = HCF(205,147) = HCF(557,205) .
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Frequently Asked Questions on HCF of 205, 557 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 205, 557?
Answer: HCF of 205, 557 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 205, 557 using Euclid's Algorithm?
Answer: For arbitrary numbers 205, 557 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.