Highest Common Factor of 406, 683, 103 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 406, 683, 103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 406, 683, 103 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 406, 683, 103 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 406, 683, 103 is 1.

HCF(406, 683, 103) = 1

HCF of 406, 683, 103 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 406, 683, 103 is 1.

Highest Common Factor of 406,683,103 using Euclid's algorithm

Highest Common Factor of 406,683,103 is 1

Step 1: Since 683 > 406, we apply the division lemma to 683 and 406, to get

683 = 406 x 1 + 277

Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 277 and 406, to get

406 = 277 x 1 + 129

Step 3: We consider the new divisor 277 and the new remainder 129, and apply the division lemma to get

277 = 129 x 2 + 19

We consider the new divisor 129 and the new remainder 19,and apply the division lemma to get

129 = 19 x 6 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 406 and 683 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(129,19) = HCF(277,129) = HCF(406,277) = HCF(683,406) .

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

Step 1: Since 103 > 1, we apply the division lemma to 103 and 1, to get

103 = 1 x 103 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 103 is 1

Notice that 1 = HCF(103,1) .

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Frequently Asked Questions on HCF of 406, 683, 103 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 406, 683, 103?

Answer: HCF of 406, 683, 103 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 406, 683, 103 using Euclid's Algorithm?

Answer: For arbitrary numbers 406, 683, 103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.