Highest Common Factor of 1026, 1703 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 1026, 1703 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1026, 1703 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 1026, 1703 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 1026, 1703 is 1.

HCF(1026, 1703) = 1

HCF of 1026, 1703 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 1026, 1703 is 1.

Highest Common Factor of 1026,1703 using Euclid's algorithm

Highest Common Factor of 1026,1703 is 1

Step 1: Since 1703 > 1026, we apply the division lemma to 1703 and 1026, to get

1703 = 1026 x 1 + 677

Step 2: Since the reminder 1026 ≠ 0, we apply division lemma to 677 and 1026, to get

1026 = 677 x 1 + 349

Step 3: We consider the new divisor 677 and the new remainder 349, and apply the division lemma to get

677 = 349 x 1 + 328

We consider the new divisor 349 and the new remainder 328,and apply the division lemma to get

349 = 328 x 1 + 21

We consider the new divisor 328 and the new remainder 21,and apply the division lemma to get

328 = 21 x 15 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1026 and 1703 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(328,21) = HCF(349,328) = HCF(677,349) = HCF(1026,677) = HCF(1703,1026) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 1026, 1703 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 1026, 1703?

Answer: HCF of 1026, 1703 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1026, 1703 using Euclid's Algorithm?

Answer: For arbitrary numbers 1026, 1703 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.