Highest Common Factor of 557, 221, 691 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 557, 221, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 557, 221, 691 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 557, 221, 691 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 557, 221, 691 is 1.

HCF(557, 221, 691) = 1

HCF of 557, 221, 691 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 557, 221, 691 is 1.

Highest Common Factor of 557,221,691 using Euclid's algorithm

Highest Common Factor of 557,221,691 is 1

Step 1: Since 557 > 221, we apply the division lemma to 557 and 221, to get

557 = 221 x 2 + 115

Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 115 and 221, to get

221 = 115 x 1 + 106

Step 3: We consider the new divisor 115 and the new remainder 106, and apply the division lemma to get

115 = 106 x 1 + 9

We consider the new divisor 106 and the new remainder 9,and apply the division lemma to get

106 = 9 x 11 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 557 and 221 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(106,9) = HCF(115,106) = HCF(221,115) = HCF(557,221) .

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

Step 1: Since 691 > 1, we apply the division lemma to 691 and 1, to get

691 = 1 x 691 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 691 is 1

Notice that 1 = HCF(691,1) .

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Frequently Asked Questions on HCF of 557, 221, 691 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 557, 221, 691?

Answer: HCF of 557, 221, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 557, 221, 691 using Euclid's Algorithm?

Answer: For arbitrary numbers 557, 221, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.