Highest Common Factor of 585, 817, 209 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 585, 817, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 585, 817, 209 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 585, 817, 209 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 585, 817, 209 is 1.
HCF(585, 817, 209) = 1
HCF of 585, 817, 209 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 585, 817, 209 is 1.
Highest Common Factor of 585,817,209 is 1
Step 1: Since 817 > 585, we apply the division lemma to 817 and 585, to get
817 = 585 x 1 + 232
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 232 and 585, to get
585 = 232 x 2 + 121
Step 3: We consider the new divisor 232 and the new remainder 121, and apply the division lemma to get
232 = 121 x 1 + 111
We consider the new divisor 121 and the new remainder 111,and apply the division lemma to get
121 = 111 x 1 + 10
We consider the new divisor 111 and the new remainder 10,and apply the division lemma to get
111 = 10 x 11 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 585 and 817 is 1
Notice that 1 = HCF(10,1) = HCF(111,10) = HCF(121,111) = HCF(232,121) = HCF(585,232) = HCF(817,585) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 209 > 1, we apply the division lemma to 209 and 1, to get
209 = 1 x 209 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 209 is 1
Notice that 1 = HCF(209,1) .
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Frequently Asked Questions on HCF of 585, 817, 209 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 585, 817, 209?
Answer: HCF of 585, 817, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 585, 817, 209 using Euclid's Algorithm?
Answer: For arbitrary numbers 585, 817, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.