Highest Common Factor of 684, 387, 269 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 684, 387, 269 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 684, 387, 269 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 684, 387, 269 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 684, 387, 269 is 1.

HCF(684, 387, 269) = 1

HCF of 684, 387, 269 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 684, 387, 269 is 1.

Highest Common Factor of 684,387,269 using Euclid's algorithm

Highest Common Factor of 684,387,269 is 1

Step 1: Since 684 > 387, we apply the division lemma to 684 and 387, to get

684 = 387 x 1 + 297

Step 2: Since the reminder 387 ≠ 0, we apply division lemma to 297 and 387, to get

387 = 297 x 1 + 90

Step 3: We consider the new divisor 297 and the new remainder 90, and apply the division lemma to get

297 = 90 x 3 + 27

We consider the new divisor 90 and the new remainder 27,and apply the division lemma to get

90 = 27 x 3 + 9

We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get

27 = 9 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 684 and 387 is 9

Notice that 9 = HCF(27,9) = HCF(90,27) = HCF(297,90) = HCF(387,297) = HCF(684,387) .

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

Step 1: Since 269 > 9, we apply the division lemma to 269 and 9, to get

269 = 9 x 29 + 8

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 8 and 9, to get

9 = 8 x 1 + 1

Step 3: We consider the new divisor 8 and the new remainder 1, and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 269 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(269,9) .

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Frequently Asked Questions on HCF of 684, 387, 269 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 684, 387, 269?

Answer: HCF of 684, 387, 269 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 684, 387, 269 using Euclid's Algorithm?

Answer: For arbitrary numbers 684, 387, 269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.