Highest Common Factor of 966, 671, 381 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 966, 671, 381 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 966, 671, 381 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 966, 671, 381 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 966, 671, 381 is 1.

HCF(966, 671, 381) = 1

HCF of 966, 671, 381 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 966, 671, 381 is 1.

Highest Common Factor of 966,671,381 using Euclid's algorithm

Highest Common Factor of 966,671,381 is 1

Step 1: Since 966 > 671, we apply the division lemma to 966 and 671, to get

966 = 671 x 1 + 295

Step 2: Since the reminder 671 ≠ 0, we apply division lemma to 295 and 671, to get

671 = 295 x 2 + 81

Step 3: We consider the new divisor 295 and the new remainder 81, and apply the division lemma to get

295 = 81 x 3 + 52

We consider the new divisor 81 and the new remainder 52,and apply the division lemma to get

81 = 52 x 1 + 29

We consider the new divisor 52 and the new remainder 29,and apply the division lemma to get

52 = 29 x 1 + 23

We consider the new divisor 29 and the new remainder 23,and apply the division lemma to get

29 = 23 x 1 + 6

We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get

23 = 6 x 3 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 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 966 and 671 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(29,23) = HCF(52,29) = HCF(81,52) = HCF(295,81) = HCF(671,295) = HCF(966,671) .

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

Step 1: Since 381 > 1, we apply the division lemma to 381 and 1, to get

381 = 1 x 381 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 381 is 1

Notice that 1 = HCF(381,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 966, 671, 381 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 966, 671, 381?

Answer: HCF of 966, 671, 381 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 966, 671, 381 using Euclid's Algorithm?

Answer: For arbitrary numbers 966, 671, 381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.