Highest Common Factor of 557, 684, 916 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, 684, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 557, 684, 916 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, 684, 916 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, 684, 916 is 1.

HCF(557, 684, 916) = 1

HCF of 557, 684, 916 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, 684, 916 is 1.

Highest Common Factor of 557,684,916 using Euclid's algorithm

Highest Common Factor of 557,684,916 is 1

Step 1: Since 684 > 557, we apply the division lemma to 684 and 557, to get

684 = 557 x 1 + 127

Step 2: Since the reminder 557 ≠ 0, we apply division lemma to 127 and 557, to get

557 = 127 x 4 + 49

Step 3: We consider the new divisor 127 and the new remainder 49, and apply the division lemma to get

127 = 49 x 2 + 29

We consider the new divisor 49 and the new remainder 29,and apply the division lemma to get

49 = 29 x 1 + 20

We consider the new divisor 29 and the new remainder 20,and apply the division lemma to get

29 = 20 x 1 + 9

We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get

20 = 9 x 2 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 684 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(29,20) = HCF(49,29) = HCF(127,49) = HCF(557,127) = HCF(684,557) .

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

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

916 = 1 x 916 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 916 is 1

Notice that 1 = HCF(916,1) .

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Frequently Asked Questions on HCF of 557, 684, 916 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, 684, 916?

Answer: HCF of 557, 684, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 557, 684, 916 using Euclid's Algorithm?

Answer: For arbitrary numbers 557, 684, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.