Highest Common Factor of 1221, 6527 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 1221, 6527 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1221, 6527 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 1221, 6527 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 1221, 6527 is 1.

HCF(1221, 6527) = 1

HCF of 1221, 6527 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 1221, 6527 is 1.

Highest Common Factor of 1221,6527 using Euclid's algorithm

Highest Common Factor of 1221,6527 is 1

Step 1: Since 6527 > 1221, we apply the division lemma to 6527 and 1221, to get

6527 = 1221 x 5 + 422

Step 2: Since the reminder 1221 ≠ 0, we apply division lemma to 422 and 1221, to get

1221 = 422 x 2 + 377

Step 3: We consider the new divisor 422 and the new remainder 377, and apply the division lemma to get

422 = 377 x 1 + 45

We consider the new divisor 377 and the new remainder 45,and apply the division lemma to get

377 = 45 x 8 + 17

We consider the new divisor 45 and the new remainder 17,and apply the division lemma to get

45 = 17 x 2 + 11

We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get

17 = 11 x 1 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1221 and 6527 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(45,17) = HCF(377,45) = HCF(422,377) = HCF(1221,422) = HCF(6527,1221) .

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Frequently Asked Questions on HCF of 1221, 6527 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 1221, 6527?

Answer: HCF of 1221, 6527 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1221, 6527 using Euclid's Algorithm?

Answer: For arbitrary numbers 1221, 6527 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.