Highest Common Factor of 5506, 6691 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 5506, 6691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5506, 6691 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 5506, 6691 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 5506, 6691 is 1.

HCF(5506, 6691) = 1

HCF of 5506, 6691 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 5506, 6691 is 1.

Highest Common Factor of 5506,6691 using Euclid's algorithm

Highest Common Factor of 5506,6691 is 1

Step 1: Since 6691 > 5506, we apply the division lemma to 6691 and 5506, to get

6691 = 5506 x 1 + 1185

Step 2: Since the reminder 5506 ≠ 0, we apply division lemma to 1185 and 5506, to get

5506 = 1185 x 4 + 766

Step 3: We consider the new divisor 1185 and the new remainder 766, and apply the division lemma to get

1185 = 766 x 1 + 419

We consider the new divisor 766 and the new remainder 419,and apply the division lemma to get

766 = 419 x 1 + 347

We consider the new divisor 419 and the new remainder 347,and apply the division lemma to get

419 = 347 x 1 + 72

We consider the new divisor 347 and the new remainder 72,and apply the division lemma to get

347 = 72 x 4 + 59

We consider the new divisor 72 and the new remainder 59,and apply the division lemma to get

72 = 59 x 1 + 13

We consider the new divisor 59 and the new remainder 13,and apply the division lemma to get

59 = 13 x 4 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5506 and 6691 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(59,13) = HCF(72,59) = HCF(347,72) = HCF(419,347) = HCF(766,419) = HCF(1185,766) = HCF(5506,1185) = HCF(6691,5506) .

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Frequently Asked Questions on HCF of 5506, 6691 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 5506, 6691?

Answer: HCF of 5506, 6691 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5506, 6691 using Euclid's Algorithm?

Answer: For arbitrary numbers 5506, 6691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.