Highest Common Factor of 563, 354 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, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 563, 354 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, 354 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, 354 is 1.

HCF(563, 354) = 1

HCF of 563, 354 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, 354 is 1.

Highest Common Factor of 563,354 using Euclid's algorithm

Highest Common Factor of 563,354 is 1

Step 1: Since 563 > 354, we apply the division lemma to 563 and 354, to get

563 = 354 x 1 + 209

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 209 and 354, to get

354 = 209 x 1 + 145

Step 3: We consider the new divisor 209 and the new remainder 145, and apply the division lemma to get

209 = 145 x 1 + 64

We consider the new divisor 145 and the new remainder 64,and apply the division lemma to get

145 = 64 x 2 + 17

We consider the new divisor 64 and the new remainder 17,and apply the division lemma to get

64 = 17 x 3 + 13

We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get

17 = 13 x 1 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 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 563 and 354 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(64,17) = HCF(145,64) = HCF(209,145) = HCF(354,209) = HCF(563,354) .

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Frequently Asked Questions on HCF of 563, 354 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, 354?

Answer: HCF of 563, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 563, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 563, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.