Highest Common Factor of 704, 10243 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 704, 10243 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 704, 10243 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 704, 10243 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 704, 10243 is 1.

HCF(704, 10243) = 1

HCF of 704, 10243 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 704, 10243 is 1.

Highest Common Factor of 704,10243 using Euclid's algorithm

Highest Common Factor of 704,10243 is 1

Step 1: Since 10243 > 704, we apply the division lemma to 10243 and 704, to get

10243 = 704 x 14 + 387

Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 387 and 704, to get

704 = 387 x 1 + 317

Step 3: We consider the new divisor 387 and the new remainder 317, and apply the division lemma to get

387 = 317 x 1 + 70

We consider the new divisor 317 and the new remainder 70,and apply the division lemma to get

317 = 70 x 4 + 37

We consider the new divisor 70 and the new remainder 37,and apply the division lemma to get

70 = 37 x 1 + 33

We consider the new divisor 37 and the new remainder 33,and apply the division lemma to get

37 = 33 x 1 + 4

We consider the new divisor 33 and the new remainder 4,and apply the division lemma to get

33 = 4 x 8 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 704 and 10243 is 1

Notice that 1 = HCF(4,1) = HCF(33,4) = HCF(37,33) = HCF(70,37) = HCF(317,70) = HCF(387,317) = HCF(704,387) = HCF(10243,704) .

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Frequently Asked Questions on HCF of 704, 10243 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 704, 10243?

Answer: HCF of 704, 10243 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 704, 10243 using Euclid's Algorithm?

Answer: For arbitrary numbers 704, 10243 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.