Highest Common Factor of 274, 512, 430 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 274, 512, 430 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 274, 512, 430 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 274, 512, 430 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 274, 512, 430 is 2.

HCF(274, 512, 430) = 2

HCF of 274, 512, 430 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 274, 512, 430 is 2.

Highest Common Factor of 274,512,430 using Euclid's algorithm

Highest Common Factor of 274,512,430 is 2

Step 1: Since 512 > 274, we apply the division lemma to 512 and 274, to get

512 = 274 x 1 + 238

Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 238 and 274, to get

274 = 238 x 1 + 36

Step 3: We consider the new divisor 238 and the new remainder 36, and apply the division lemma to get

238 = 36 x 6 + 22

We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get

36 = 22 x 1 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 274 and 512 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(238,36) = HCF(274,238) = HCF(512,274) .

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

Step 1: Since 430 > 2, we apply the division lemma to 430 and 2, to get

430 = 2 x 215 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 430 is 2

Notice that 2 = HCF(430,2) .

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Frequently Asked Questions on HCF of 274, 512, 430 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 274, 512, 430?

Answer: HCF of 274, 512, 430 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 274, 512, 430 using Euclid's Algorithm?

Answer: For arbitrary numbers 274, 512, 430 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.