Highest Common Factor of 469, 305, 489 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 469, 305, 489 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 469, 305, 489 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 469, 305, 489 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 469, 305, 489 is 1.

HCF(469, 305, 489) = 1

HCF of 469, 305, 489 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 469, 305, 489 is 1.

Highest Common Factor of 469,305,489 using Euclid's algorithm

Highest Common Factor of 469,305,489 is 1

Step 1: Since 469 > 305, we apply the division lemma to 469 and 305, to get

469 = 305 x 1 + 164

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 164 and 305, to get

305 = 164 x 1 + 141

Step 3: We consider the new divisor 164 and the new remainder 141, and apply the division lemma to get

164 = 141 x 1 + 23

We consider the new divisor 141 and the new remainder 23,and apply the division lemma to get

141 = 23 x 6 + 3

We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get

23 = 3 x 7 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 469 and 305 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(141,23) = HCF(164,141) = HCF(305,164) = HCF(469,305) .

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

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

489 = 1 x 489 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 489 is 1

Notice that 1 = HCF(489,1) .

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Frequently Asked Questions on HCF of 469, 305, 489 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 469, 305, 489?

Answer: HCF of 469, 305, 489 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 469, 305, 489 using Euclid's Algorithm?

Answer: For arbitrary numbers 469, 305, 489 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.