Highest Common Factor of 557, 905, 188 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, 905, 188 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 557, 905, 188 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, 905, 188 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, 905, 188 is 1.

HCF(557, 905, 188) = 1

HCF of 557, 905, 188 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, 905, 188 is 1.

Highest Common Factor of 557,905,188 using Euclid's algorithm

Highest Common Factor of 557,905,188 is 1

Step 1: Since 905 > 557, we apply the division lemma to 905 and 557, to get

905 = 557 x 1 + 348

Step 2: Since the reminder 557 ≠ 0, we apply division lemma to 348 and 557, to get

557 = 348 x 1 + 209

Step 3: We consider the new divisor 348 and the new remainder 209, and apply the division lemma to get

348 = 209 x 1 + 139

We consider the new divisor 209 and the new remainder 139,and apply the division lemma to get

209 = 139 x 1 + 70

We consider the new divisor 139 and the new remainder 70,and apply the division lemma to get

139 = 70 x 1 + 69

We consider the new divisor 70 and the new remainder 69,and apply the division lemma to get

70 = 69 x 1 + 1

We consider the new divisor 69 and the new remainder 1,and apply the division lemma to get

69 = 1 x 69 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 557 and 905 is 1

Notice that 1 = HCF(69,1) = HCF(70,69) = HCF(139,70) = HCF(209,139) = HCF(348,209) = HCF(557,348) = HCF(905,557) .

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

Step 1: Since 188 > 1, we apply the division lemma to 188 and 1, to get

188 = 1 x 188 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 188 is 1

Notice that 1 = HCF(188,1) .

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Frequently Asked Questions on HCF of 557, 905, 188 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, 905, 188?

Answer: HCF of 557, 905, 188 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 557, 905, 188 using Euclid's Algorithm?

Answer: For arbitrary numbers 557, 905, 188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.