Highest Common Factor of 557, 884, 361 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, 884, 361 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 557, 884, 361 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, 884, 361 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, 884, 361 is 1.

HCF(557, 884, 361) = 1

HCF of 557, 884, 361 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, 884, 361 is 1.

Highest Common Factor of 557,884,361 using Euclid's algorithm

Highest Common Factor of 557,884,361 is 1

Step 1: Since 884 > 557, we apply the division lemma to 884 and 557, to get

884 = 557 x 1 + 327

Step 2: Since the reminder 557 ≠ 0, we apply division lemma to 327 and 557, to get

557 = 327 x 1 + 230

Step 3: We consider the new divisor 327 and the new remainder 230, and apply the division lemma to get

327 = 230 x 1 + 97

We consider the new divisor 230 and the new remainder 97,and apply the division lemma to get

230 = 97 x 2 + 36

We consider the new divisor 97 and the new remainder 36,and apply the division lemma to get

97 = 36 x 2 + 25

We consider the new divisor 36 and the new remainder 25,and apply the division lemma to get

36 = 25 x 1 + 11

We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get

25 = 11 x 2 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 884 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(36,25) = HCF(97,36) = HCF(230,97) = HCF(327,230) = HCF(557,327) = HCF(884,557) .

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

Step 1: Since 361 > 1, we apply the division lemma to 361 and 1, to get

361 = 1 x 361 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 361 is 1

Notice that 1 = HCF(361,1) .

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Frequently Asked Questions on HCF of 557, 884, 361 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, 884, 361?

Answer: HCF of 557, 884, 361 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 557, 884, 361 using Euclid's Algorithm?

Answer: For arbitrary numbers 557, 884, 361 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.