Highest Common Factor of 966, 612, 17 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, 612, 17 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 966, 612, 17 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, 612, 17 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, 612, 17 is 1.

HCF(966, 612, 17) = 1

HCF of 966, 612, 17 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, 612, 17 is 1.

Highest Common Factor of 966,612,17 using Euclid's algorithm

Highest Common Factor of 966,612,17 is 1

Step 1: Since 966 > 612, we apply the division lemma to 966 and 612, to get

966 = 612 x 1 + 354

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 354 and 612, to get

612 = 354 x 1 + 258

Step 3: We consider the new divisor 354 and the new remainder 258, and apply the division lemma to get

354 = 258 x 1 + 96

We consider the new divisor 258 and the new remainder 96,and apply the division lemma to get

258 = 96 x 2 + 66

We consider the new divisor 96 and the new remainder 66,and apply the division lemma to get

96 = 66 x 1 + 30

We consider the new divisor 66 and the new remainder 30,and apply the division lemma to get

66 = 30 x 2 + 6

We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get

30 = 6 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 966 and 612 is 6

Notice that 6 = HCF(30,6) = HCF(66,30) = HCF(96,66) = HCF(258,96) = HCF(354,258) = HCF(612,354) = HCF(966,612) .

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

Step 1: Since 17 > 6, we apply the division lemma to 17 and 6, to get

17 = 6 x 2 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: 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 6 and 17 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) .

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, 612, 17 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, 612, 17?

Answer: HCF of 966, 612, 17 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 966, 612, 17 using Euclid's Algorithm?

Answer: For arbitrary numbers 966, 612, 17 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.