Highest Common Factor of 685, 994, 419 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 685, 994, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 994, 419 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 685, 994, 419 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 685, 994, 419 is 1.

HCF(685, 994, 419) = 1

HCF of 685, 994, 419 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 685, 994, 419 is 1.

Highest Common Factor of 685,994,419 using Euclid's algorithm

Highest Common Factor of 685,994,419 is 1

Step 1: Since 994 > 685, we apply the division lemma to 994 and 685, to get

994 = 685 x 1 + 309

Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 309 and 685, to get

685 = 309 x 2 + 67

Step 3: We consider the new divisor 309 and the new remainder 67, and apply the division lemma to get

309 = 67 x 4 + 41

We consider the new divisor 67 and the new remainder 41,and apply the division lemma to get

67 = 41 x 1 + 26

We consider the new divisor 41 and the new remainder 26,and apply the division lemma to get

41 = 26 x 1 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 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 685 and 994 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(41,26) = HCF(67,41) = HCF(309,67) = HCF(685,309) = HCF(994,685) .

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

Step 1: Since 419 > 1, we apply the division lemma to 419 and 1, to get

419 = 1 x 419 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 419 is 1

Notice that 1 = HCF(419,1) .

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Frequently Asked Questions on HCF of 685, 994, 419 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 685, 994, 419?

Answer: HCF of 685, 994, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 994, 419 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 994, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.