Highest Common Factor of 5665, 6577 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 5665, 6577 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5665, 6577 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 5665, 6577 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 5665, 6577 is 1.

HCF(5665, 6577) = 1

HCF of 5665, 6577 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 5665, 6577 is 1.

Highest Common Factor of 5665,6577 using Euclid's algorithm

Highest Common Factor of 5665,6577 is 1

Step 1: Since 6577 > 5665, we apply the division lemma to 6577 and 5665, to get

6577 = 5665 x 1 + 912

Step 2: Since the reminder 5665 ≠ 0, we apply division lemma to 912 and 5665, to get

5665 = 912 x 6 + 193

Step 3: We consider the new divisor 912 and the new remainder 193, and apply the division lemma to get

912 = 193 x 4 + 140

We consider the new divisor 193 and the new remainder 140,and apply the division lemma to get

193 = 140 x 1 + 53

We consider the new divisor 140 and the new remainder 53,and apply the division lemma to get

140 = 53 x 2 + 34

We consider the new divisor 53 and the new remainder 34,and apply the division lemma to get

53 = 34 x 1 + 19

We consider the new divisor 34 and the new remainder 19,and apply the division lemma to get

34 = 19 x 1 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 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 5665 and 6577 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(34,19) = HCF(53,34) = HCF(140,53) = HCF(193,140) = HCF(912,193) = HCF(5665,912) = HCF(6577,5665) .

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Frequently Asked Questions on HCF of 5665, 6577 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 5665, 6577?

Answer: HCF of 5665, 6577 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5665, 6577 using Euclid's Algorithm?

Answer: For arbitrary numbers 5665, 6577 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.