Highest Common Factor of 657, 288, 218 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 657, 288, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 657, 288, 218 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 657, 288, 218 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 657, 288, 218 is 1.

HCF(657, 288, 218) = 1

HCF of 657, 288, 218 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 657, 288, 218 is 1.

Highest Common Factor of 657,288,218 using Euclid's algorithm

Highest Common Factor of 657,288,218 is 1

Step 1: Since 657 > 288, we apply the division lemma to 657 and 288, to get

657 = 288 x 2 + 81

Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 81 and 288, to get

288 = 81 x 3 + 45

Step 3: We consider the new divisor 81 and the new remainder 45, and apply the division lemma to get

81 = 45 x 1 + 36

We consider the new divisor 45 and the new remainder 36,and apply the division lemma to get

45 = 36 x 1 + 9

We consider the new divisor 36 and the new remainder 9,and apply the division lemma to get

36 = 9 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 657 and 288 is 9

Notice that 9 = HCF(36,9) = HCF(45,36) = HCF(81,45) = HCF(288,81) = HCF(657,288) .

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

Step 1: Since 218 > 9, we apply the division lemma to 218 and 9, to get

218 = 9 x 24 + 2

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 2 and 9, to get

9 = 2 x 4 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 9 and 218 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(218,9) .

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Frequently Asked Questions on HCF of 657, 288, 218 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 657, 288, 218?

Answer: HCF of 657, 288, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 657, 288, 218 using Euclid's Algorithm?

Answer: For arbitrary numbers 657, 288, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.