Highest Common Factor of 420, 667, 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 420, 667, 489 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 667, 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 420, 667, 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 420, 667, 489 is 1.

HCF(420, 667, 489) = 1

HCF of 420, 667, 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 420, 667, 489 is 1.

Highest Common Factor of 420,667,489 using Euclid's algorithm

Highest Common Factor of 420,667,489 is 1

Step 1: Since 667 > 420, we apply the division lemma to 667 and 420, to get

667 = 420 x 1 + 247

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 247 and 420, to get

420 = 247 x 1 + 173

Step 3: We consider the new divisor 247 and the new remainder 173, and apply the division lemma to get

247 = 173 x 1 + 74

We consider the new divisor 173 and the new remainder 74,and apply the division lemma to get

173 = 74 x 2 + 25

We consider the new divisor 74 and the new remainder 25,and apply the division lemma to get

74 = 25 x 2 + 24

We consider the new divisor 25 and the new remainder 24,and apply the division lemma to get

25 = 24 x 1 + 1

We consider the new divisor 24 and the new remainder 1,and apply the division lemma to get

24 = 1 x 24 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 420 and 667 is 1

Notice that 1 = HCF(24,1) = HCF(25,24) = HCF(74,25) = HCF(173,74) = HCF(247,173) = HCF(420,247) = HCF(667,420) .

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 420, 667, 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 420, 667, 489?

Answer: HCF of 420, 667, 489 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 667, 489 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 667, 489 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.