Highest Common Factor of 269, 414, 857 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 269, 414, 857 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 269, 414, 857 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 269, 414, 857 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 269, 414, 857 is 1.

HCF(269, 414, 857) = 1

HCF of 269, 414, 857 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 269, 414, 857 is 1.

Highest Common Factor of 269,414,857 using Euclid's algorithm

Highest Common Factor of 269,414,857 is 1

Step 1: Since 414 > 269, we apply the division lemma to 414 and 269, to get

414 = 269 x 1 + 145

Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 145 and 269, to get

269 = 145 x 1 + 124

Step 3: We consider the new divisor 145 and the new remainder 124, and apply the division lemma to get

145 = 124 x 1 + 21

We consider the new divisor 124 and the new remainder 21,and apply the division lemma to get

124 = 21 x 5 + 19

We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get

21 = 19 x 1 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 269 and 414 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(124,21) = HCF(145,124) = HCF(269,145) = HCF(414,269) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 857 > 1, we apply the division lemma to 857 and 1, to get

857 = 1 x 857 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 857 is 1

Notice that 1 = HCF(857,1) .

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Frequently Asked Questions on HCF of 269, 414, 857 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 269, 414, 857?

Answer: HCF of 269, 414, 857 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 269, 414, 857 using Euclid's Algorithm?

Answer: For arbitrary numbers 269, 414, 857 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.