Highest Common Factor of 685, 386, 781 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, 386, 781 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 386, 781 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, 386, 781 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, 386, 781 is 1.

HCF(685, 386, 781) = 1

HCF of 685, 386, 781 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, 386, 781 is 1.

Highest Common Factor of 685,386,781 using Euclid's algorithm

Highest Common Factor of 685,386,781 is 1

Step 1: Since 685 > 386, we apply the division lemma to 685 and 386, to get

685 = 386 x 1 + 299

Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 299 and 386, to get

386 = 299 x 1 + 87

Step 3: We consider the new divisor 299 and the new remainder 87, and apply the division lemma to get

299 = 87 x 3 + 38

We consider the new divisor 87 and the new remainder 38,and apply the division lemma to get

87 = 38 x 2 + 11

We consider the new divisor 38 and the new remainder 11,and apply the division lemma to get

38 = 11 x 3 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 685 and 386 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(38,11) = HCF(87,38) = HCF(299,87) = HCF(386,299) = HCF(685,386) .

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

Step 1: Since 781 > 1, we apply the division lemma to 781 and 1, to get

781 = 1 x 781 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 781 is 1

Notice that 1 = HCF(781,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 685, 386, 781 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, 386, 781?

Answer: HCF of 685, 386, 781 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 386, 781 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 386, 781 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.