Highest Common Factor of 489, 406, 416 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, 406, 416 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 489, 406, 416 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, 406, 416 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, 406, 416 is 1.

HCF(489, 406, 416) = 1

HCF of 489, 406, 416 using Euclid's algorithm

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

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Highest common factor (HCF) of 489, 406, 416 is 1.

Highest Common Factor of 489,406,416 using Euclid's algorithm

Highest Common Factor of 489,406,416 is 1

Step 1: Since 489 > 406, we apply the division lemma to 489 and 406, to get

489 = 406 x 1 + 83

Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 83 and 406, to get

406 = 83 x 4 + 74

Step 3: We consider the new divisor 83 and the new remainder 74, and apply the division lemma to get

83 = 74 x 1 + 9

We consider the new divisor 74 and the new remainder 9,and apply the division lemma to get

74 = 9 x 8 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 489 and 406 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(74,9) = HCF(83,74) = HCF(406,83) = HCF(489,406) .

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

Step 1: Since 416 > 1, we apply the division lemma to 416 and 1, to get

416 = 1 x 416 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 416 is 1

Notice that 1 = HCF(416,1) .

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Frequently Asked Questions on HCF of 489, 406, 416 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, 406, 416?

Answer: HCF of 489, 406, 416 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 489, 406, 416 using Euclid's Algorithm?

Answer: For arbitrary numbers 489, 406, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.