Highest Common Factor of 343, 590, 981 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 343, 590, 981 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 343, 590, 981 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 343, 590, 981 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 343, 590, 981 is 1.

HCF(343, 590, 981) = 1

HCF of 343, 590, 981 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 343, 590, 981 is 1.

Highest Common Factor of 343,590,981 using Euclid's algorithm

Highest Common Factor of 343,590,981 is 1

Step 1: Since 590 > 343, we apply the division lemma to 590 and 343, to get

590 = 343 x 1 + 247

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 247 and 343, to get

343 = 247 x 1 + 96

Step 3: We consider the new divisor 247 and the new remainder 96, and apply the division lemma to get

247 = 96 x 2 + 55

We consider the new divisor 96 and the new remainder 55,and apply the division lemma to get

96 = 55 x 1 + 41

We consider the new divisor 55 and the new remainder 41,and apply the division lemma to get

55 = 41 x 1 + 14

We consider the new divisor 41 and the new remainder 14,and apply the division lemma to get

41 = 14 x 2 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 343 and 590 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(41,14) = HCF(55,41) = HCF(96,55) = HCF(247,96) = HCF(343,247) = HCF(590,343) .

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

Step 1: Since 981 > 1, we apply the division lemma to 981 and 1, to get

981 = 1 x 981 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 981 is 1

Notice that 1 = HCF(981,1) .

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Frequently Asked Questions on HCF of 343, 590, 981 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 343, 590, 981?

Answer: HCF of 343, 590, 981 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 343, 590, 981 using Euclid's Algorithm?

Answer: For arbitrary numbers 343, 590, 981 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.