Highest Common Factor of 217, 358, 728 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 217, 358, 728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 217, 358, 728 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 217, 358, 728 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 217, 358, 728 is 1.

HCF(217, 358, 728) = 1

HCF of 217, 358, 728 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 217, 358, 728 is 1.

Highest Common Factor of 217,358,728 using Euclid's algorithm

Highest Common Factor of 217,358,728 is 1

Step 1: Since 358 > 217, we apply the division lemma to 358 and 217, to get

358 = 217 x 1 + 141

Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 141 and 217, to get

217 = 141 x 1 + 76

Step 3: We consider the new divisor 141 and the new remainder 76, and apply the division lemma to get

141 = 76 x 1 + 65

We consider the new divisor 76 and the new remainder 65,and apply the division lemma to get

76 = 65 x 1 + 11

We consider the new divisor 65 and the new remainder 11,and apply the division lemma to get

65 = 11 x 5 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 217 and 358 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(65,11) = HCF(76,65) = HCF(141,76) = HCF(217,141) = HCF(358,217) .

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

Step 1: Since 728 > 1, we apply the division lemma to 728 and 1, to get

728 = 1 x 728 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 728 is 1

Notice that 1 = HCF(728,1) .

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Frequently Asked Questions on HCF of 217, 358, 728 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 217, 358, 728?

Answer: HCF of 217, 358, 728 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 217, 358, 728 using Euclid's Algorithm?

Answer: For arbitrary numbers 217, 358, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.