Highest Common Factor of 272, 474, 234 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 272, 474, 234 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 272, 474, 234 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 272, 474, 234 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 272, 474, 234 is 2.

HCF(272, 474, 234) = 2

HCF of 272, 474, 234 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 272, 474, 234 is 2.

Highest Common Factor of 272,474,234 using Euclid's algorithm

Highest Common Factor of 272,474,234 is 2

Step 1: Since 474 > 272, we apply the division lemma to 474 and 272, to get

474 = 272 x 1 + 202

Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 202 and 272, to get

272 = 202 x 1 + 70

Step 3: We consider the new divisor 202 and the new remainder 70, and apply the division lemma to get

202 = 70 x 2 + 62

We consider the new divisor 70 and the new remainder 62,and apply the division lemma to get

70 = 62 x 1 + 8

We consider the new divisor 62 and the new remainder 8,and apply the division lemma to get

62 = 8 x 7 + 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 272 and 474 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(62,8) = HCF(70,62) = HCF(202,70) = HCF(272,202) = HCF(474,272) .

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

Step 1: Since 234 > 2, we apply the division lemma to 234 and 2, to get

234 = 2 x 117 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 234 is 2

Notice that 2 = HCF(234,2) .

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Frequently Asked Questions on HCF of 272, 474, 234 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 272, 474, 234?

Answer: HCF of 272, 474, 234 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 272, 474, 234 using Euclid's Algorithm?

Answer: For arbitrary numbers 272, 474, 234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.