Highest Common Factor of 741, 478, 348 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 741, 478, 348 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 741, 478, 348 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 741, 478, 348 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 741, 478, 348 is 1.

HCF(741, 478, 348) = 1

HCF of 741, 478, 348 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 741, 478, 348 is 1.

Highest Common Factor of 741,478,348 using Euclid's algorithm

Highest Common Factor of 741,478,348 is 1

Step 1: Since 741 > 478, we apply the division lemma to 741 and 478, to get

741 = 478 x 1 + 263

Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 263 and 478, to get

478 = 263 x 1 + 215

Step 3: We consider the new divisor 263 and the new remainder 215, and apply the division lemma to get

263 = 215 x 1 + 48

We consider the new divisor 215 and the new remainder 48,and apply the division lemma to get

215 = 48 x 4 + 23

We consider the new divisor 48 and the new remainder 23,and apply the division lemma to get

48 = 23 x 2 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 1

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 741 and 478 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(48,23) = HCF(215,48) = HCF(263,215) = HCF(478,263) = HCF(741,478) .

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

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

348 = 1 x 348 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 348 is 1

Notice that 1 = HCF(348,1) .

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Frequently Asked Questions on HCF of 741, 478, 348 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 741, 478, 348?

Answer: HCF of 741, 478, 348 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 741, 478, 348 using Euclid's Algorithm?

Answer: For arbitrary numbers 741, 478, 348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.