Highest Common Factor of 703, 6040 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 703, 6040 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 703, 6040 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 703, 6040 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 703, 6040 is 1.

HCF(703, 6040) = 1

HCF of 703, 6040 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 703, 6040 is 1.

Highest Common Factor of 703,6040 using Euclid's algorithm

Highest Common Factor of 703,6040 is 1

Step 1: Since 6040 > 703, we apply the division lemma to 6040 and 703, to get

6040 = 703 x 8 + 416

Step 2: Since the reminder 703 ≠ 0, we apply division lemma to 416 and 703, to get

703 = 416 x 1 + 287

Step 3: We consider the new divisor 416 and the new remainder 287, and apply the division lemma to get

416 = 287 x 1 + 129

We consider the new divisor 287 and the new remainder 129,and apply the division lemma to get

287 = 129 x 2 + 29

We consider the new divisor 129 and the new remainder 29,and apply the division lemma to get

129 = 29 x 4 + 13

We consider the new divisor 29 and the new remainder 13,and apply the division lemma to get

29 = 13 x 2 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 703 and 6040 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(129,29) = HCF(287,129) = HCF(416,287) = HCF(703,416) = HCF(6040,703) .

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Frequently Asked Questions on HCF of 703, 6040 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 703, 6040?

Answer: HCF of 703, 6040 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 703, 6040 using Euclid's Algorithm?

Answer: For arbitrary numbers 703, 6040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.