Highest Common Factor of 655, 360, 873, 81 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 655, 360, 873, 81 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 655, 360, 873, 81 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 655, 360, 873, 81 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 655, 360, 873, 81 is 1.

HCF(655, 360, 873, 81) = 1

HCF of 655, 360, 873, 81 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 655, 360, 873, 81 is 1.

Highest Common Factor of 655,360,873,81 using Euclid's algorithm

Highest Common Factor of 655,360,873,81 is 1

Step 1: Since 655 > 360, we apply the division lemma to 655 and 360, to get

655 = 360 x 1 + 295

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 295 and 360, to get

360 = 295 x 1 + 65

Step 3: We consider the new divisor 295 and the new remainder 65, and apply the division lemma to get

295 = 65 x 4 + 35

We consider the new divisor 65 and the new remainder 35,and apply the division lemma to get

65 = 35 x 1 + 30

We consider the new divisor 35 and the new remainder 30,and apply the division lemma to get

35 = 30 x 1 + 5

We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get

30 = 5 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 655 and 360 is 5

Notice that 5 = HCF(30,5) = HCF(35,30) = HCF(65,35) = HCF(295,65) = HCF(360,295) = HCF(655,360) .

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

Step 1: Since 873 > 5, we apply the division lemma to 873 and 5, to get

873 = 5 x 174 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 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 5 and 873 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(873,5) .

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

Step 1: Since 81 > 1, we apply the division lemma to 81 and 1, to get

81 = 1 x 81 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 81 is 1

Notice that 1 = HCF(81,1) .

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Frequently Asked Questions on HCF of 655, 360, 873, 81 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 655, 360, 873, 81?

Answer: HCF of 655, 360, 873, 81 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 655, 360, 873, 81 using Euclid's Algorithm?

Answer: For arbitrary numbers 655, 360, 873, 81 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.