Highest Common Factor of 705, 966, 991 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 705, 966, 991 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 705, 966, 991 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 705, 966, 991 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 705, 966, 991 is 1.

HCF(705, 966, 991) = 1

HCF of 705, 966, 991 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 705, 966, 991 is 1.

Highest Common Factor of 705,966,991 using Euclid's algorithm

Highest Common Factor of 705,966,991 is 1

Step 1: Since 966 > 705, we apply the division lemma to 966 and 705, to get

966 = 705 x 1 + 261

Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 261 and 705, to get

705 = 261 x 2 + 183

Step 3: We consider the new divisor 261 and the new remainder 183, and apply the division lemma to get

261 = 183 x 1 + 78

We consider the new divisor 183 and the new remainder 78,and apply the division lemma to get

183 = 78 x 2 + 27

We consider the new divisor 78 and the new remainder 27,and apply the division lemma to get

78 = 27 x 2 + 24

We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get

27 = 24 x 1 + 3

We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get

24 = 3 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 705 and 966 is 3

Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(78,27) = HCF(183,78) = HCF(261,183) = HCF(705,261) = HCF(966,705) .

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

Step 1: Since 991 > 3, we apply the division lemma to 991 and 3, to get

991 = 3 x 330 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 991 is 1

Notice that 1 = HCF(3,1) = HCF(991,3) .

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Frequently Asked Questions on HCF of 705, 966, 991 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 705, 966, 991?

Answer: HCF of 705, 966, 991 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 705, 966, 991 using Euclid's Algorithm?

Answer: For arbitrary numbers 705, 966, 991 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.