Highest Common Factor of 8008, 1751 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 8008, 1751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8008, 1751 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 8008, 1751 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 8008, 1751 is 1.

HCF(8008, 1751) = 1

HCF of 8008, 1751 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 8008, 1751 is 1.

Highest Common Factor of 8008,1751 using Euclid's algorithm

Highest Common Factor of 8008,1751 is 1

Step 1: Since 8008 > 1751, we apply the division lemma to 8008 and 1751, to get

8008 = 1751 x 4 + 1004

Step 2: Since the reminder 1751 ≠ 0, we apply division lemma to 1004 and 1751, to get

1751 = 1004 x 1 + 747

Step 3: We consider the new divisor 1004 and the new remainder 747, and apply the division lemma to get

1004 = 747 x 1 + 257

We consider the new divisor 747 and the new remainder 257,and apply the division lemma to get

747 = 257 x 2 + 233

We consider the new divisor 257 and the new remainder 233,and apply the division lemma to get

257 = 233 x 1 + 24

We consider the new divisor 233 and the new remainder 24,and apply the division lemma to get

233 = 24 x 9 + 17

We consider the new divisor 24 and the new remainder 17,and apply the division lemma to get

24 = 17 x 1 + 7

We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get

17 = 7 x 2 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 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 8008 and 1751 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(233,24) = HCF(257,233) = HCF(747,257) = HCF(1004,747) = HCF(1751,1004) = HCF(8008,1751) .

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Frequently Asked Questions on HCF of 8008, 1751 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 8008, 1751?

Answer: HCF of 8008, 1751 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8008, 1751 using Euclid's Algorithm?

Answer: For arbitrary numbers 8008, 1751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.