Highest Common Factor of 344, 840, 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 344, 840, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 344, 840, 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 344, 840, 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 344, 840, 343 is 1.

HCF(344, 840, 343) = 1

HCF of 344, 840, 343 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 344, 840, 343 is 1.

Highest Common Factor of 344,840,343 using Euclid's algorithm

Highest Common Factor of 344,840,343 is 1

Step 1: Since 840 > 344, we apply the division lemma to 840 and 344, to get

840 = 344 x 2 + 152

Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 152 and 344, to get

344 = 152 x 2 + 40

Step 3: We consider the new divisor 152 and the new remainder 40, and apply the division lemma to get

152 = 40 x 3 + 32

We consider the new divisor 40 and the new remainder 32,and apply the division lemma to get

40 = 32 x 1 + 8

We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get

32 = 8 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 344 and 840 is 8

Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(152,40) = HCF(344,152) = HCF(840,344) .

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

Step 1: Since 343 > 8, we apply the division lemma to 343 and 8, to get

343 = 8 x 42 + 7

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 7 and 8, to get

8 = 7 x 1 + 1

Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 343 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(343,8) .

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Frequently Asked Questions on HCF of 344, 840, 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 344, 840, 343?

Answer: HCF of 344, 840, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 344, 840, 343 using Euclid's Algorithm?

Answer: For arbitrary numbers 344, 840, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.