Highest Common Factor of 545, 872, 494 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 545, 872, 494 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 545, 872, 494 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 545, 872, 494 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 545, 872, 494 is 1.

HCF(545, 872, 494) = 1

HCF of 545, 872, 494 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 545, 872, 494 is 1.

Highest Common Factor of 545,872,494 using Euclid's algorithm

Highest Common Factor of 545,872,494 is 1

Step 1: Since 872 > 545, we apply the division lemma to 872 and 545, to get

872 = 545 x 1 + 327

Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 327 and 545, to get

545 = 327 x 1 + 218

Step 3: We consider the new divisor 327 and the new remainder 218, and apply the division lemma to get

327 = 218 x 1 + 109

We consider the new divisor 218 and the new remainder 109, and apply the division lemma to get

218 = 109 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 109, the HCF of 545 and 872 is 109

Notice that 109 = HCF(218,109) = HCF(327,218) = HCF(545,327) = HCF(872,545) .

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

Step 1: Since 494 > 109, we apply the division lemma to 494 and 109, to get

494 = 109 x 4 + 58

Step 2: Since the reminder 109 ≠ 0, we apply division lemma to 58 and 109, to get

109 = 58 x 1 + 51

Step 3: We consider the new divisor 58 and the new remainder 51, and apply the division lemma to get

58 = 51 x 1 + 7

We consider the new divisor 51 and the new remainder 7,and apply the division lemma to get

51 = 7 x 7 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 109 and 494 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(51,7) = HCF(58,51) = HCF(109,58) = HCF(494,109) .

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Frequently Asked Questions on HCF of 545, 872, 494 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 545, 872, 494?

Answer: HCF of 545, 872, 494 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 545, 872, 494 using Euclid's Algorithm?

Answer: For arbitrary numbers 545, 872, 494 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.