Highest Common Factor of 663, 225, 289 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 663, 225, 289 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 225, 289 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 663, 225, 289 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 663, 225, 289 is 1.

HCF(663, 225, 289) = 1

HCF of 663, 225, 289 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 663, 225, 289 is 1.

Highest Common Factor of 663,225,289 using Euclid's algorithm

Highest Common Factor of 663,225,289 is 1

Step 1: Since 663 > 225, we apply the division lemma to 663 and 225, to get

663 = 225 x 2 + 213

Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 213 and 225, to get

225 = 213 x 1 + 12

Step 3: We consider the new divisor 213 and the new remainder 12, and apply the division lemma to get

213 = 12 x 17 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 663 and 225 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(213,12) = HCF(225,213) = HCF(663,225) .

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

Step 1: Since 289 > 3, we apply the division lemma to 289 and 3, to get

289 = 3 x 96 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 289 is 1

Notice that 1 = HCF(3,1) = HCF(289,3) .

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Frequently Asked Questions on HCF of 663, 225, 289 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 663, 225, 289?

Answer: HCF of 663, 225, 289 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 225, 289 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 225, 289 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.