Highest Common Factor of 346, 544, 343 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 346, 544, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 346, 544, 343 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 346, 544, 343 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 346, 544, 343 is 1.

HCF(346, 544, 343) = 1

HCF of 346, 544, 343 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 346, 544, 343 is 1.

Highest Common Factor of 346,544,343 using Euclid's algorithm

Highest Common Factor of 346,544,343 is 1

Step 1: Since 544 > 346, we apply the division lemma to 544 and 346, to get

544 = 346 x 1 + 198

Step 2: Since the reminder 346 ≠ 0, we apply division lemma to 198 and 346, to get

346 = 198 x 1 + 148

Step 3: We consider the new divisor 198 and the new remainder 148, and apply the division lemma to get

198 = 148 x 1 + 50

We consider the new divisor 148 and the new remainder 50,and apply the division lemma to get

148 = 50 x 2 + 48

We consider the new divisor 50 and the new remainder 48,and apply the division lemma to get

50 = 48 x 1 + 2

We consider the new divisor 48 and the new remainder 2,and apply the division lemma to get

48 = 2 x 24 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 346 and 544 is 2

Notice that 2 = HCF(48,2) = HCF(50,48) = HCF(148,50) = HCF(198,148) = HCF(346,198) = HCF(544,346) .

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

Step 1: Since 343 > 2, we apply the division lemma to 343 and 2, to get

343 = 2 x 171 + 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 343 is 1

Notice that 1 = HCF(2,1) = HCF(343,2) .

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Frequently Asked Questions on HCF of 346, 544, 343 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 346, 544, 343?

Answer: HCF of 346, 544, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 346, 544, 343 using Euclid's Algorithm?

Answer: For arbitrary numbers 346, 544, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.