Highest Common Factor of 463, 725, 288 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 463, 725, 288 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 463, 725, 288 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 463, 725, 288 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 463, 725, 288 is 1.

HCF(463, 725, 288) = 1

HCF of 463, 725, 288 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 463, 725, 288 is 1.

Highest Common Factor of 463,725,288 using Euclid's algorithm

Highest Common Factor of 463,725,288 is 1

Step 1: Since 725 > 463, we apply the division lemma to 725 and 463, to get

725 = 463 x 1 + 262

Step 2: Since the reminder 463 ≠ 0, we apply division lemma to 262 and 463, to get

463 = 262 x 1 + 201

Step 3: We consider the new divisor 262 and the new remainder 201, and apply the division lemma to get

262 = 201 x 1 + 61

We consider the new divisor 201 and the new remainder 61,and apply the division lemma to get

201 = 61 x 3 + 18

We consider the new divisor 61 and the new remainder 18,and apply the division lemma to get

61 = 18 x 3 + 7

We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get

18 = 7 x 2 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

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

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 463 and 725 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(61,18) = HCF(201,61) = HCF(262,201) = HCF(463,262) = HCF(725,463) .

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

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

288 = 1 x 288 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 288 is 1

Notice that 1 = HCF(288,1) .

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Frequently Asked Questions on HCF of 463, 725, 288 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 463, 725, 288?

Answer: HCF of 463, 725, 288 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 463, 725, 288 using Euclid's Algorithm?

Answer: For arbitrary numbers 463, 725, 288 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.