Highest Common Factor of 558, 413 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 558, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 558, 413 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 558, 413 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 558, 413 is 1.
HCF(558, 413) = 1
HCF of 558, 413 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 558, 413 is 1.
Highest Common Factor of 558,413 is 1
Step 1: Since 558 > 413, we apply the division lemma to 558 and 413, to get
558 = 413 x 1 + 145
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 145 and 413, to get
413 = 145 x 2 + 123
Step 3: We consider the new divisor 145 and the new remainder 123, and apply the division lemma to get
145 = 123 x 1 + 22
We consider the new divisor 123 and the new remainder 22,and apply the division lemma to get
123 = 22 x 5 + 13
We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get
22 = 13 x 1 + 9
We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get
13 = 9 x 1 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 558 and 413 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(123,22) = HCF(145,123) = HCF(413,145) = HCF(558,413) .
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Frequently Asked Questions on HCF of 558, 413 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 558, 413?
Answer: HCF of 558, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 558, 413 using Euclid's Algorithm?
Answer: For arbitrary numbers 558, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.