Highest Common Factor of 709, 968, 377 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, 968, 377 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 709, 968, 377 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, 968, 377 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, 968, 377 is 1.

HCF(709, 968, 377) = 1

HCF of 709, 968, 377 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, 968, 377 is 1.

Highest Common Factor of 709,968,377 using Euclid's algorithm

Highest Common Factor of 709,968,377 is 1

Step 1: Since 968 > 709, we apply the division lemma to 968 and 709, to get

968 = 709 x 1 + 259

Step 2: Since the reminder 709 ≠ 0, we apply division lemma to 259 and 709, to get

709 = 259 x 2 + 191

Step 3: We consider the new divisor 259 and the new remainder 191, and apply the division lemma to get

259 = 191 x 1 + 68

We consider the new divisor 191 and the new remainder 68,and apply the division lemma to get

191 = 68 x 2 + 55

We consider the new divisor 68 and the new remainder 55,and apply the division lemma to get

68 = 55 x 1 + 13

We consider the new divisor 55 and the new remainder 13,and apply the division lemma to get

55 = 13 x 4 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 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 709 and 968 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(55,13) = HCF(68,55) = HCF(191,68) = HCF(259,191) = HCF(709,259) = HCF(968,709) .

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

Step 1: Since 377 > 1, we apply the division lemma to 377 and 1, to get

377 = 1 x 377 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 377 is 1

Notice that 1 = HCF(377,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 709, 968, 377 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, 968, 377?

Answer: HCF of 709, 968, 377 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 709, 968, 377 using Euclid's Algorithm?

Answer: For arbitrary numbers 709, 968, 377 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.