Highest Common Factor of 209, 657, 85 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 209, 657, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 209, 657, 85 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 209, 657, 85 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 209, 657, 85 is 1.
HCF(209, 657, 85) = 1
HCF of 209, 657, 85 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 209, 657, 85 is 1.
Highest Common Factor of 209,657,85 is 1
Step 1: Since 657 > 209, we apply the division lemma to 657 and 209, to get
657 = 209 x 3 + 30
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 30 and 209, to get
209 = 30 x 6 + 29
Step 3: We consider the new divisor 30 and the new remainder 29, and apply the division lemma to get
30 = 29 x 1 + 1
We consider the new divisor 29 and the new remainder 1, and apply the division lemma to get
29 = 1 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 209 and 657 is 1
Notice that 1 = HCF(29,1) = HCF(30,29) = HCF(209,30) = HCF(657,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85 > 1, we apply the division lemma to 85 and 1, to get
85 = 1 x 85 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 85 is 1
Notice that 1 = HCF(85,1) .
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Frequently Asked Questions on HCF of 209, 657, 85 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 209, 657, 85?
Answer: HCF of 209, 657, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 209, 657, 85 using Euclid's Algorithm?
Answer: For arbitrary numbers 209, 657, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.