Highest Common Factor of 268, 708, 366 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 268, 708, 366 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 268, 708, 366 is 2 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 268, 708, 366 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 268, 708, 366 is 2.

HCF(268, 708, 366) = 2

HCF of 268, 708, 366 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 268, 708, 366 is 2.

Highest Common Factor of 268,708,366 using Euclid's algorithm

Highest Common Factor of 268,708,366 is 2

Step 1: Since 708 > 268, we apply the division lemma to 708 and 268, to get

708 = 268 x 2 + 172

Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 172 and 268, to get

268 = 172 x 1 + 96

Step 3: We consider the new divisor 172 and the new remainder 96, and apply the division lemma to get

172 = 96 x 1 + 76

We consider the new divisor 96 and the new remainder 76,and apply the division lemma to get

96 = 76 x 1 + 20

We consider the new divisor 76 and the new remainder 20,and apply the division lemma to get

76 = 20 x 3 + 16

We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get

20 = 16 x 1 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 268 and 708 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(76,20) = HCF(96,76) = HCF(172,96) = HCF(268,172) = HCF(708,268) .

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

Step 1: Since 366 > 4, we apply the division lemma to 366 and 4, to get

366 = 4 x 91 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 366 is 2

Notice that 2 = HCF(4,2) = HCF(366,4) .

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Frequently Asked Questions on HCF of 268, 708, 366 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 268, 708, 366?

Answer: HCF of 268, 708, 366 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 268, 708, 366 using Euclid's Algorithm?

Answer: For arbitrary numbers 268, 708, 366 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.