Highest Common Factor of 557, 4021 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, 4021 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 557, 4021 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, 4021 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, 4021 is 1.
HCF(557, 4021) = 1
HCF of 557, 4021 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, 4021 is 1.
Highest Common Factor of 557,4021 is 1
Step 1: Since 4021 > 557, we apply the division lemma to 4021 and 557, to get
4021 = 557 x 7 + 122
Step 2: Since the reminder 557 ≠ 0, we apply division lemma to 122 and 557, to get
557 = 122 x 4 + 69
Step 3: We consider the new divisor 122 and the new remainder 69, and apply the division lemma to get
122 = 69 x 1 + 53
We consider the new divisor 69 and the new remainder 53,and apply the division lemma to get
69 = 53 x 1 + 16
We consider the new divisor 53 and the new remainder 16,and apply the division lemma to get
53 = 16 x 3 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 557 and 4021 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(53,16) = HCF(69,53) = HCF(122,69) = HCF(557,122) = HCF(4021,557) .
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Frequently Asked Questions on HCF of 557, 4021 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, 4021?
Answer: HCF of 557, 4021 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 557, 4021 using Euclid's Algorithm?
Answer: For arbitrary numbers 557, 4021 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.