Highest Common Factor of 617, 403, 68 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 617, 403, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 617, 403, 68 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 617, 403, 68 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 617, 403, 68 is 1.

HCF(617, 403, 68) = 1

HCF of 617, 403, 68 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 617, 403, 68 is 1.

Highest Common Factor of 617,403,68 using Euclid's algorithm

Highest Common Factor of 617,403,68 is 1

Step 1: Since 617 > 403, we apply the division lemma to 617 and 403, to get

617 = 403 x 1 + 214

Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 214 and 403, to get

403 = 214 x 1 + 189

Step 3: We consider the new divisor 214 and the new remainder 189, and apply the division lemma to get

214 = 189 x 1 + 25

We consider the new divisor 189 and the new remainder 25,and apply the division lemma to get

189 = 25 x 7 + 14

We consider the new divisor 25 and the new remainder 14,and apply the division lemma to get

25 = 14 x 1 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 617 and 403 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(189,25) = HCF(214,189) = HCF(403,214) = HCF(617,403) .

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

Step 1: Since 68 > 1, we apply the division lemma to 68 and 1, to get

68 = 1 x 68 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1

Notice that 1 = HCF(68,1) .

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Frequently Asked Questions on HCF of 617, 403, 68 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 617, 403, 68?

Answer: HCF of 617, 403, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 617, 403, 68 using Euclid's Algorithm?

Answer: For arbitrary numbers 617, 403, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.