Highest Common Factor of 489, 348, 267, 614 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 489, 348, 267, 614 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 489, 348, 267, 614 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 489, 348, 267, 614 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 489, 348, 267, 614 is 1.

HCF(489, 348, 267, 614) = 1

HCF of 489, 348, 267, 614 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 489, 348, 267, 614 is 1.

Highest Common Factor of 489,348,267,614 using Euclid's algorithm

Highest Common Factor of 489,348,267,614 is 1

Step 1: Since 489 > 348, we apply the division lemma to 489 and 348, to get

489 = 348 x 1 + 141

Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 141 and 348, to get

348 = 141 x 2 + 66

Step 3: We consider the new divisor 141 and the new remainder 66, and apply the division lemma to get

141 = 66 x 2 + 9

We consider the new divisor 66 and the new remainder 9,and apply the division lemma to get

66 = 9 x 7 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 489 and 348 is 3

Notice that 3 = HCF(9,3) = HCF(66,9) = HCF(141,66) = HCF(348,141) = HCF(489,348) .

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

Step 1: Since 267 > 3, we apply the division lemma to 267 and 3, to get

267 = 3 x 89 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 267 is 3

Notice that 3 = HCF(267,3) .

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

Step 1: Since 614 > 3, we apply the division lemma to 614 and 3, to get

614 = 3 x 204 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 614 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(614,3) .

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Frequently Asked Questions on HCF of 489, 348, 267, 614 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 489, 348, 267, 614?

Answer: HCF of 489, 348, 267, 614 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 489, 348, 267, 614 using Euclid's Algorithm?

Answer: For arbitrary numbers 489, 348, 267, 614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.