Highest Common Factor of 288, 463, 197 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, 463, 197 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 288, 463, 197 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 288, 463, 197 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, 463, 197 is 1.

HCF(288, 463, 197) = 1

HCF of 288, 463, 197 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 288, 463, 197 is 1.

Highest Common Factor of 288,463,197 using Euclid's algorithm

Highest Common Factor of 288,463,197 is 1

Step 1: Since 463 > 288, we apply the division lemma to 463 and 288, to get

463 = 288 x 1 + 175

Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 175 and 288, to get

288 = 175 x 1 + 113

Step 3: We consider the new divisor 175 and the new remainder 113, and apply the division lemma to get

175 = 113 x 1 + 62

We consider the new divisor 113 and the new remainder 62,and apply the division lemma to get

113 = 62 x 1 + 51

We consider the new divisor 62 and the new remainder 51,and apply the division lemma to get

62 = 51 x 1 + 11

We consider the new divisor 51 and the new remainder 11,and apply the division lemma to get

51 = 11 x 4 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 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 288 and 463 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(51,11) = HCF(62,51) = HCF(113,62) = HCF(175,113) = HCF(288,175) = HCF(463,288) .

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

Step 1: Since 197 > 1, we apply the division lemma to 197 and 1, to get

197 = 1 x 197 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 197 is 1

Notice that 1 = HCF(197,1) .

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Frequently Asked Questions on HCF of 288, 463, 197 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, 463, 197?

Answer: HCF of 288, 463, 197 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 288, 463, 197 using Euclid's Algorithm?

Answer: For arbitrary numbers 288, 463, 197 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.