Highest Common Factor of 345, 563, 279 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 345, 563, 279 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 345, 563, 279 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 345, 563, 279 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 345, 563, 279 is 1.

HCF(345, 563, 279) = 1

HCF of 345, 563, 279 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 345, 563, 279 is 1.

Highest Common Factor of 345,563,279 using Euclid's algorithm

Highest Common Factor of 345,563,279 is 1

Step 1: Since 563 > 345, we apply the division lemma to 563 and 345, to get

563 = 345 x 1 + 218

Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 218 and 345, to get

345 = 218 x 1 + 127

Step 3: We consider the new divisor 218 and the new remainder 127, and apply the division lemma to get

218 = 127 x 1 + 91

We consider the new divisor 127 and the new remainder 91,and apply the division lemma to get

127 = 91 x 1 + 36

We consider the new divisor 91 and the new remainder 36,and apply the division lemma to get

91 = 36 x 2 + 19

We consider the new divisor 36 and the new remainder 19,and apply the division lemma to get

36 = 19 x 1 + 17

We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get

19 = 17 x 1 + 2

We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get

17 = 2 x 8 + 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 345 and 563 is 1

Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(36,19) = HCF(91,36) = HCF(127,91) = HCF(218,127) = HCF(345,218) = HCF(563,345) .

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

Step 1: Since 279 > 1, we apply the division lemma to 279 and 1, to get

279 = 1 x 279 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 279 is 1

Notice that 1 = HCF(279,1) .

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Frequently Asked Questions on HCF of 345, 563, 279 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 345, 563, 279?

Answer: HCF of 345, 563, 279 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 345, 563, 279 using Euclid's Algorithm?

Answer: For arbitrary numbers 345, 563, 279 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.