Highest Common Factor of 375, 586, 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 375, 586, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 375, 586, 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 375, 586, 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 375, 586, 209 is 1.
HCF(375, 586, 209) = 1
HCF of 375, 586, 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 375, 586, 209 is 1.
Highest Common Factor of 375,586,209 is 1
Step 1: Since 586 > 375, we apply the division lemma to 586 and 375, to get
586 = 375 x 1 + 211
Step 2: Since the reminder 375 ≠ 0, we apply division lemma to 211 and 375, to get
375 = 211 x 1 + 164
Step 3: We consider the new divisor 211 and the new remainder 164, and apply the division lemma to get
211 = 164 x 1 + 47
We consider the new divisor 164 and the new remainder 47,and apply the division lemma to get
164 = 47 x 3 + 23
We consider the new divisor 47 and the new remainder 23,and apply the division lemma to get
47 = 23 x 2 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 375 and 586 is 1
Notice that 1 = HCF(23,1) = HCF(47,23) = HCF(164,47) = HCF(211,164) = HCF(375,211) = HCF(586,375) .
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 375, 586, 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 375, 586, 209?
Answer: HCF of 375, 586, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 375, 586, 209 using Euclid's Algorithm?
Answer: For arbitrary numbers 375, 586, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
