Highest Common Factor of 225, 306, 274 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 225, 306, 274 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 225, 306, 274 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 225, 306, 274 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 225, 306, 274 is 1.

HCF(225, 306, 274) = 1

HCF of 225, 306, 274 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 225, 306, 274 is 1.

Highest Common Factor of 225,306,274 using Euclid's algorithm

Highest Common Factor of 225,306,274 is 1

Step 1: Since 306 > 225, we apply the division lemma to 306 and 225, to get

306 = 225 x 1 + 81

Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 81 and 225, to get

225 = 81 x 2 + 63

Step 3: We consider the new divisor 81 and the new remainder 63, and apply the division lemma to get

81 = 63 x 1 + 18

We consider the new divisor 63 and the new remainder 18,and apply the division lemma to get

63 = 18 x 3 + 9

We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 225 and 306 is 9

Notice that 9 = HCF(18,9) = HCF(63,18) = HCF(81,63) = HCF(225,81) = HCF(306,225) .

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

Step 1: Since 274 > 9, we apply the division lemma to 274 and 9, to get

274 = 9 x 30 + 4

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 4 and 9, to get

9 = 4 x 2 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 274 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(274,9) .

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Frequently Asked Questions on HCF of 225, 306, 274 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 225, 306, 274?

Answer: HCF of 225, 306, 274 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 225, 306, 274 using Euclid's Algorithm?

Answer: For arbitrary numbers 225, 306, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.