Highest Common Factor of 709, 905, 403 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 709, 905, 403 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 709, 905, 403 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 709, 905, 403 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 709, 905, 403 is 1.

HCF(709, 905, 403) = 1

HCF of 709, 905, 403 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 709, 905, 403 is 1.

Highest Common Factor of 709,905,403 using Euclid's algorithm

Highest Common Factor of 709,905,403 is 1

Step 1: Since 905 > 709, we apply the division lemma to 905 and 709, to get

905 = 709 x 1 + 196

Step 2: Since the reminder 709 ≠ 0, we apply division lemma to 196 and 709, to get

709 = 196 x 3 + 121

Step 3: We consider the new divisor 196 and the new remainder 121, and apply the division lemma to get

196 = 121 x 1 + 75

We consider the new divisor 121 and the new remainder 75,and apply the division lemma to get

121 = 75 x 1 + 46

We consider the new divisor 75 and the new remainder 46,and apply the division lemma to get

75 = 46 x 1 + 29

We consider the new divisor 46 and the new remainder 29,and apply the division lemma to get

46 = 29 x 1 + 17

We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get

29 = 17 x 1 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 709 and 905 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(46,29) = HCF(75,46) = HCF(121,75) = HCF(196,121) = HCF(709,196) = HCF(905,709) .

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

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

403 = 1 x 403 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 403 is 1

Notice that 1 = HCF(403,1) .

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Frequently Asked Questions on HCF of 709, 905, 403 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 709, 905, 403?

Answer: HCF of 709, 905, 403 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 709, 905, 403 using Euclid's Algorithm?

Answer: For arbitrary numbers 709, 905, 403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.