Highest Common Factor of 242, 328, 814 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 242, 328, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 242, 328, 814 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 242, 328, 814 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 242, 328, 814 is 2.

HCF(242, 328, 814) = 2

HCF of 242, 328, 814 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 242, 328, 814 is 2.

Highest Common Factor of 242,328,814 using Euclid's algorithm

Highest Common Factor of 242,328,814 is 2

Step 1: Since 328 > 242, we apply the division lemma to 328 and 242, to get

328 = 242 x 1 + 86

Step 2: Since the reminder 242 ≠ 0, we apply division lemma to 86 and 242, to get

242 = 86 x 2 + 70

Step 3: We consider the new divisor 86 and the new remainder 70, and apply the division lemma to get

86 = 70 x 1 + 16

We consider the new divisor 70 and the new remainder 16,and apply the division lemma to get

70 = 16 x 4 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 242 and 328 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(70,16) = HCF(86,70) = HCF(242,86) = HCF(328,242) .

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

Step 1: Since 814 > 2, we apply the division lemma to 814 and 2, to get

814 = 2 x 407 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 814 is 2

Notice that 2 = HCF(814,2) .

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Frequently Asked Questions on HCF of 242, 328, 814 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 242, 328, 814?

Answer: HCF of 242, 328, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 242, 328, 814 using Euclid's Algorithm?

Answer: For arbitrary numbers 242, 328, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.