Highest Common Factor of 529, 205 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 529, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 529, 205 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 529, 205 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 529, 205 is 1.
HCF(529, 205) = 1
HCF of 529, 205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 529, 205 is 1.
Highest Common Factor of 529,205 is 1
Step 1: Since 529 > 205, we apply the division lemma to 529 and 205, to get
529 = 205 x 2 + 119
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 119 and 205, to get
205 = 119 x 1 + 86
Step 3: We consider the new divisor 119 and the new remainder 86, and apply the division lemma to get
119 = 86 x 1 + 33
We consider the new divisor 86 and the new remainder 33,and apply the division lemma to get
86 = 33 x 2 + 20
We consider the new divisor 33 and the new remainder 20,and apply the division lemma to get
33 = 20 x 1 + 13
We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get
20 = 13 x 1 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 529 and 205 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(33,20) = HCF(86,33) = HCF(119,86) = HCF(205,119) = HCF(529,205) .
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Frequently Asked Questions on HCF of 529, 205 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 529, 205?
Answer: HCF of 529, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 529, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 529, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.