Highest Common Factor of 288, 450, 230 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 288, 450, 230 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 288, 450, 230 is 2 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 288, 450, 230 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 288, 450, 230 is 2.

HCF(288, 450, 230) = 2

HCF of 288, 450, 230 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 288, 450, 230 is 2.

Highest Common Factor of 288,450,230 using Euclid's algorithm

Highest Common Factor of 288,450,230 is 2

Step 1: Since 450 > 288, we apply the division lemma to 450 and 288, to get

450 = 288 x 1 + 162

Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 162 and 288, to get

288 = 162 x 1 + 126

Step 3: We consider the new divisor 162 and the new remainder 126, and apply the division lemma to get

162 = 126 x 1 + 36

We consider the new divisor 126 and the new remainder 36,and apply the division lemma to get

126 = 36 x 3 + 18

We consider the new divisor 36 and the new remainder 18,and apply the division lemma to get

36 = 18 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 288 and 450 is 18

Notice that 18 = HCF(36,18) = HCF(126,36) = HCF(162,126) = HCF(288,162) = HCF(450,288) .

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

Step 1: Since 230 > 18, we apply the division lemma to 230 and 18, to get

230 = 18 x 12 + 14

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 14 and 18, to get

18 = 14 x 1 + 4

Step 3: We consider the new divisor 14 and the new remainder 4, and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 230 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(230,18) .

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Frequently Asked Questions on HCF of 288, 450, 230 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 288, 450, 230?

Answer: HCF of 288, 450, 230 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 288, 450, 230 using Euclid's Algorithm?

Answer: For arbitrary numbers 288, 450, 230 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.