Highest Common Factor of 224, 810, 143 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 224, 810, 143 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 224, 810, 143 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 224, 810, 143 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 224, 810, 143 is 1.

HCF(224, 810, 143) = 1

HCF of 224, 810, 143 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 224, 810, 143 is 1.

Highest Common Factor of 224,810,143 using Euclid's algorithm

Highest Common Factor of 224,810,143 is 1

Step 1: Since 810 > 224, we apply the division lemma to 810 and 224, to get

810 = 224 x 3 + 138

Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 138 and 224, to get

224 = 138 x 1 + 86

Step 3: We consider the new divisor 138 and the new remainder 86, and apply the division lemma to get

138 = 86 x 1 + 52

We consider the new divisor 86 and the new remainder 52,and apply the division lemma to get

86 = 52 x 1 + 34

We consider the new divisor 52 and the new remainder 34,and apply the division lemma to get

52 = 34 x 1 + 18

We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get

34 = 18 x 1 + 16

We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get

18 = 16 x 1 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 224 and 810 is 2

Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(52,34) = HCF(86,52) = HCF(138,86) = HCF(224,138) = HCF(810,224) .

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

Step 1: Since 143 > 2, we apply the division lemma to 143 and 2, to get

143 = 2 x 71 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 143 is 1

Notice that 1 = HCF(2,1) = HCF(143,2) .

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Frequently Asked Questions on HCF of 224, 810, 143 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 224, 810, 143?

Answer: HCF of 224, 810, 143 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 224, 810, 143 using Euclid's Algorithm?

Answer: For arbitrary numbers 224, 810, 143 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.