Highest Common Factor of 735, 465, 227 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 735, 465, 227 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 735, 465, 227 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 735, 465, 227 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 735, 465, 227 is 1.

HCF(735, 465, 227) = 1

HCF of 735, 465, 227 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 735, 465, 227 is 1.

Highest Common Factor of 735,465,227 using Euclid's algorithm

Highest Common Factor of 735,465,227 is 1

Step 1: Since 735 > 465, we apply the division lemma to 735 and 465, to get

735 = 465 x 1 + 270

Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 270 and 465, to get

465 = 270 x 1 + 195

Step 3: We consider the new divisor 270 and the new remainder 195, and apply the division lemma to get

270 = 195 x 1 + 75

We consider the new divisor 195 and the new remainder 75,and apply the division lemma to get

195 = 75 x 2 + 45

We consider the new divisor 75 and the new remainder 45,and apply the division lemma to get

75 = 45 x 1 + 30

We consider the new divisor 45 and the new remainder 30,and apply the division lemma to get

45 = 30 x 1 + 15

We consider the new divisor 30 and the new remainder 15,and apply the division lemma to get

30 = 15 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 735 and 465 is 15

Notice that 15 = HCF(30,15) = HCF(45,30) = HCF(75,45) = HCF(195,75) = HCF(270,195) = HCF(465,270) = HCF(735,465) .

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

Step 1: Since 227 > 15, we apply the division lemma to 227 and 15, to get

227 = 15 x 15 + 2

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 2 and 15, to get

15 = 2 x 7 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 227 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(227,15) .

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Frequently Asked Questions on HCF of 735, 465, 227 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 735, 465, 227?

Answer: HCF of 735, 465, 227 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 735, 465, 227 using Euclid's Algorithm?

Answer: For arbitrary numbers 735, 465, 227 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.