Highest Common Factor of 561, 916, 557 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 561, 916, 557 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 561, 916, 557 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 561, 916, 557 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 561, 916, 557 is 1.

HCF(561, 916, 557) = 1

HCF of 561, 916, 557 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 561, 916, 557 is 1.

Highest Common Factor of 561,916,557 using Euclid's algorithm

Highest Common Factor of 561,916,557 is 1

Step 1: Since 916 > 561, we apply the division lemma to 916 and 561, to get

916 = 561 x 1 + 355

Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 355 and 561, to get

561 = 355 x 1 + 206

Step 3: We consider the new divisor 355 and the new remainder 206, and apply the division lemma to get

355 = 206 x 1 + 149

We consider the new divisor 206 and the new remainder 149,and apply the division lemma to get

206 = 149 x 1 + 57

We consider the new divisor 149 and the new remainder 57,and apply the division lemma to get

149 = 57 x 2 + 35

We consider the new divisor 57 and the new remainder 35,and apply the division lemma to get

57 = 35 x 1 + 22

We consider the new divisor 35 and the new remainder 22,and apply the division lemma to get

35 = 22 x 1 + 13

We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get

22 = 13 x 1 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 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 561 and 916 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(35,22) = HCF(57,35) = HCF(149,57) = HCF(206,149) = HCF(355,206) = HCF(561,355) = HCF(916,561) .

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

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

557 = 1 x 557 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 557 is 1

Notice that 1 = HCF(557,1) .

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Frequently Asked Questions on HCF of 561, 916, 557 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 561, 916, 557?

Answer: HCF of 561, 916, 557 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 561, 916, 557 using Euclid's Algorithm?

Answer: For arbitrary numbers 561, 916, 557 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.