Highest Common Factor of 348, 618, 103 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 348, 618, 103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 348, 618, 103 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 348, 618, 103 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 348, 618, 103 is 1.

HCF(348, 618, 103) = 1

HCF of 348, 618, 103 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 348, 618, 103 is 1.

Highest Common Factor of 348,618,103 using Euclid's algorithm

Highest Common Factor of 348,618,103 is 1

Step 1: Since 618 > 348, we apply the division lemma to 618 and 348, to get

618 = 348 x 1 + 270

Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 270 and 348, to get

348 = 270 x 1 + 78

Step 3: We consider the new divisor 270 and the new remainder 78, and apply the division lemma to get

270 = 78 x 3 + 36

We consider the new divisor 78 and the new remainder 36,and apply the division lemma to get

78 = 36 x 2 + 6

We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get

36 = 6 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 348 and 618 is 6

Notice that 6 = HCF(36,6) = HCF(78,36) = HCF(270,78) = HCF(348,270) = HCF(618,348) .

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

Step 1: Since 103 > 6, we apply the division lemma to 103 and 6, to get

103 = 6 x 17 + 1

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 103 is 1

Notice that 1 = HCF(6,1) = HCF(103,6) .

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Frequently Asked Questions on HCF of 348, 618, 103 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 348, 618, 103?

Answer: HCF of 348, 618, 103 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 348, 618, 103 using Euclid's Algorithm?

Answer: For arbitrary numbers 348, 618, 103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.