Highest Common Factor of 563, 906, 182 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 563, 906, 182 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 563, 906, 182 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 563, 906, 182 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 563, 906, 182 is 1.

HCF(563, 906, 182) = 1

HCF of 563, 906, 182 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 563, 906, 182 is 1.

Highest Common Factor of 563,906,182 using Euclid's algorithm

Highest Common Factor of 563,906,182 is 1

Step 1: Since 906 > 563, we apply the division lemma to 906 and 563, to get

906 = 563 x 1 + 343

Step 2: Since the reminder 563 ≠ 0, we apply division lemma to 343 and 563, to get

563 = 343 x 1 + 220

Step 3: We consider the new divisor 343 and the new remainder 220, and apply the division lemma to get

343 = 220 x 1 + 123

We consider the new divisor 220 and the new remainder 123,and apply the division lemma to get

220 = 123 x 1 + 97

We consider the new divisor 123 and the new remainder 97,and apply the division lemma to get

123 = 97 x 1 + 26

We consider the new divisor 97 and the new remainder 26,and apply the division lemma to get

97 = 26 x 3 + 19

We consider the new divisor 26 and the new remainder 19,and apply the division lemma to get

26 = 19 x 1 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 563 and 906 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(26,19) = HCF(97,26) = HCF(123,97) = HCF(220,123) = HCF(343,220) = HCF(563,343) = HCF(906,563) .

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

Step 1: Since 182 > 1, we apply the division lemma to 182 and 1, to get

182 = 1 x 182 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 182 is 1

Notice that 1 = HCF(182,1) .

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Frequently Asked Questions on HCF of 563, 906, 182 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 563, 906, 182?

Answer: HCF of 563, 906, 182 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 563, 906, 182 using Euclid's Algorithm?

Answer: For arbitrary numbers 563, 906, 182 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.