Highest Common Factor of 343, 659, 884 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, 659, 884 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 343, 659, 884 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, 659, 884 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, 659, 884 is 1.

HCF(343, 659, 884) = 1

HCF of 343, 659, 884 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, 659, 884 is 1.

Highest Common Factor of 343,659,884 using Euclid's algorithm

Highest Common Factor of 343,659,884 is 1

Step 1: Since 659 > 343, we apply the division lemma to 659 and 343, to get

659 = 343 x 1 + 316

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 316 and 343, to get

343 = 316 x 1 + 27

Step 3: We consider the new divisor 316 and the new remainder 27, and apply the division lemma to get

316 = 27 x 11 + 19

We consider the new divisor 27 and the new remainder 19,and apply the division lemma to get

27 = 19 x 1 + 8

We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get

19 = 8 x 2 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 343 and 659 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(316,27) = HCF(343,316) = HCF(659,343) .

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

Step 1: Since 884 > 1, we apply the division lemma to 884 and 1, to get

884 = 1 x 884 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 884 is 1

Notice that 1 = HCF(884,1) .

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Frequently Asked Questions on HCF of 343, 659, 884 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, 659, 884?

Answer: HCF of 343, 659, 884 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 343, 659, 884 using Euclid's Algorithm?

Answer: For arbitrary numbers 343, 659, 884 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.