Highest Common Factor of 354, 230, 231 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 354, 230, 231 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 230, 231 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 354, 230, 231 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 354, 230, 231 is 1.

HCF(354, 230, 231) = 1

HCF of 354, 230, 231 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 354, 230, 231 is 1.

Highest Common Factor of 354,230,231 using Euclid's algorithm

Highest Common Factor of 354,230,231 is 1

Step 1: Since 354 > 230, we apply the division lemma to 354 and 230, to get

354 = 230 x 1 + 124

Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 124 and 230, to get

230 = 124 x 1 + 106

Step 3: We consider the new divisor 124 and the new remainder 106, and apply the division lemma to get

124 = 106 x 1 + 18

We consider the new divisor 106 and the new remainder 18,and apply the division lemma to get

106 = 18 x 5 + 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 354 and 230 is 2

Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(106,18) = HCF(124,106) = HCF(230,124) = HCF(354,230) .

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

Step 1: Since 231 > 2, we apply the division lemma to 231 and 2, to get

231 = 2 x 115 + 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 231 is 1

Notice that 1 = HCF(2,1) = HCF(231,2) .

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Frequently Asked Questions on HCF of 354, 230, 231 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 354, 230, 231?

Answer: HCF of 354, 230, 231 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 230, 231 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 230, 231 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.