Highest Common Factor of 556, 6543, 1321 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 556, 6543, 1321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 556, 6543, 1321 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 556, 6543, 1321 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 556, 6543, 1321 is 1.

HCF(556, 6543, 1321) = 1

HCF of 556, 6543, 1321 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 556, 6543, 1321 is 1.

Highest Common Factor of 556,6543,1321 using Euclid's algorithm

Highest Common Factor of 556,6543,1321 is 1

Step 1: Since 6543 > 556, we apply the division lemma to 6543 and 556, to get

6543 = 556 x 11 + 427

Step 2: Since the reminder 556 ≠ 0, we apply division lemma to 427 and 556, to get

556 = 427 x 1 + 129

Step 3: We consider the new divisor 427 and the new remainder 129, and apply the division lemma to get

427 = 129 x 3 + 40

We consider the new divisor 129 and the new remainder 40,and apply the division lemma to get

129 = 40 x 3 + 9

We consider the new divisor 40 and the new remainder 9,and apply the division lemma to get

40 = 9 x 4 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 556 and 6543 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(40,9) = HCF(129,40) = HCF(427,129) = HCF(556,427) = HCF(6543,556) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 1321 > 1, we apply the division lemma to 1321 and 1, to get

1321 = 1 x 1321 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1321 is 1

Notice that 1 = HCF(1321,1) .

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Frequently Asked Questions on HCF of 556, 6543, 1321 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 556, 6543, 1321?

Answer: HCF of 556, 6543, 1321 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 556, 6543, 1321 using Euclid's Algorithm?

Answer: For arbitrary numbers 556, 6543, 1321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.