Highest Common Factor of 602, 342, 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 602, 342, 227 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 602, 342, 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 602, 342, 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 602, 342, 227 is 1.

HCF(602, 342, 227) = 1

HCF of 602, 342, 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 602, 342, 227 is 1.

Highest Common Factor of 602,342,227 using Euclid's algorithm

Highest Common Factor of 602,342,227 is 1

Step 1: Since 602 > 342, we apply the division lemma to 602 and 342, to get

602 = 342 x 1 + 260

Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 260 and 342, to get

342 = 260 x 1 + 82

Step 3: We consider the new divisor 260 and the new remainder 82, and apply the division lemma to get

260 = 82 x 3 + 14

We consider the new divisor 82 and the new remainder 14,and apply the division lemma to get

82 = 14 x 5 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 602 and 342 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(82,14) = HCF(260,82) = HCF(342,260) = HCF(602,342) .

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

Step 1: Since 227 > 2, we apply the division lemma to 227 and 2, to get

227 = 2 x 113 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 227 is 1

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

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Frequently Asked Questions on HCF of 602, 342, 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 602, 342, 227?

Answer: HCF of 602, 342, 227 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 602, 342, 227 using Euclid's Algorithm?

Answer: For arbitrary numbers 602, 342, 227 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.