Highest Common Factor of 6501, 754 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 6501, 754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6501, 754 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 6501, 754 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 6501, 754 is 1.

HCF(6501, 754) = 1

HCF of 6501, 754 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 6501, 754 is 1.

Highest Common Factor of 6501,754 using Euclid's algorithm

Highest Common Factor of 6501,754 is 1

Step 1: Since 6501 > 754, we apply the division lemma to 6501 and 754, to get

6501 = 754 x 8 + 469

Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 469 and 754, to get

754 = 469 x 1 + 285

Step 3: We consider the new divisor 469 and the new remainder 285, and apply the division lemma to get

469 = 285 x 1 + 184

We consider the new divisor 285 and the new remainder 184,and apply the division lemma to get

285 = 184 x 1 + 101

We consider the new divisor 184 and the new remainder 101,and apply the division lemma to get

184 = 101 x 1 + 83

We consider the new divisor 101 and the new remainder 83,and apply the division lemma to get

101 = 83 x 1 + 18

We consider the new divisor 83 and the new remainder 18,and apply the division lemma to get

83 = 18 x 4 + 11

We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get

18 = 11 x 1 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 6501 and 754 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(83,18) = HCF(101,83) = HCF(184,101) = HCF(285,184) = HCF(469,285) = HCF(754,469) = HCF(6501,754) .

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Frequently Asked Questions on HCF of 6501, 754 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 6501, 754?

Answer: HCF of 6501, 754 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6501, 754 using Euclid's Algorithm?

Answer: For arbitrary numbers 6501, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.