Highest Common Factor of 208, 414, 591 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 208, 414, 591 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 208, 414, 591 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 208, 414, 591 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 208, 414, 591 is 1.
HCF(208, 414, 591) = 1
HCF of 208, 414, 591 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 208, 414, 591 is 1.
Highest Common Factor of 208,414,591 is 1
Step 1: Since 414 > 208, we apply the division lemma to 414 and 208, to get
414 = 208 x 1 + 206
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 206 and 208, to get
208 = 206 x 1 + 2
Step 3: We consider the new divisor 206 and the new remainder 2, and apply the division lemma to get
206 = 2 x 103 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 208 and 414 is 2
Notice that 2 = HCF(206,2) = HCF(208,206) = HCF(414,208) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 591 > 2, we apply the division lemma to 591 and 2, to get
591 = 2 x 295 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 591 is 1
Notice that 1 = HCF(2,1) = HCF(591,2) .
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Frequently Asked Questions on HCF of 208, 414, 591 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 208, 414, 591?
Answer: HCF of 208, 414, 591 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 208, 414, 591 using Euclid's Algorithm?
Answer: For arbitrary numbers 208, 414, 591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.