Highest Common Factor of 6569, 752 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 6569, 752 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6569, 752 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 6569, 752 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 6569, 752 is 1.

HCF(6569, 752) = 1

HCF of 6569, 752 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 6569, 752 is 1.

Highest Common Factor of 6569,752 using Euclid's algorithm

Highest Common Factor of 6569,752 is 1

Step 1: Since 6569 > 752, we apply the division lemma to 6569 and 752, to get

6569 = 752 x 8 + 553

Step 2: Since the reminder 752 ≠ 0, we apply division lemma to 553 and 752, to get

752 = 553 x 1 + 199

Step 3: We consider the new divisor 553 and the new remainder 199, and apply the division lemma to get

553 = 199 x 2 + 155

We consider the new divisor 199 and the new remainder 155,and apply the division lemma to get

199 = 155 x 1 + 44

We consider the new divisor 155 and the new remainder 44,and apply the division lemma to get

155 = 44 x 3 + 23

We consider the new divisor 44 and the new remainder 23,and apply the division lemma to get

44 = 23 x 1 + 21

We consider the new divisor 23 and the new remainder 21,and apply the division lemma to get

23 = 21 x 1 + 2

We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get

21 = 2 x 10 + 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 6569 and 752 is 1

Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(44,23) = HCF(155,44) = HCF(199,155) = HCF(553,199) = HCF(752,553) = HCF(6569,752) .

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Frequently Asked Questions on HCF of 6569, 752 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 6569, 752?

Answer: HCF of 6569, 752 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6569, 752 using Euclid's Algorithm?

Answer: For arbitrary numbers 6569, 752 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.