Highest Common Factor of 343, 923, 914 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, 923, 914 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 343, 923, 914 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, 923, 914 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, 923, 914 is 1.

HCF(343, 923, 914) = 1

HCF of 343, 923, 914 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, 923, 914 is 1.

Highest Common Factor of 343,923,914 using Euclid's algorithm

Highest Common Factor of 343,923,914 is 1

Step 1: Since 923 > 343, we apply the division lemma to 923 and 343, to get

923 = 343 x 2 + 237

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 237 and 343, to get

343 = 237 x 1 + 106

Step 3: We consider the new divisor 237 and the new remainder 106, and apply the division lemma to get

237 = 106 x 2 + 25

We consider the new divisor 106 and the new remainder 25,and apply the division lemma to get

106 = 25 x 4 + 6

We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get

25 = 6 x 4 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 343 and 923 is 1

Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(106,25) = HCF(237,106) = HCF(343,237) = HCF(923,343) .

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

Step 1: Since 914 > 1, we apply the division lemma to 914 and 1, to get

914 = 1 x 914 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 914 is 1

Notice that 1 = HCF(914,1) .

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Frequently Asked Questions on HCF of 343, 923, 914 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, 923, 914?

Answer: HCF of 343, 923, 914 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 343, 923, 914 using Euclid's Algorithm?

Answer: For arbitrary numbers 343, 923, 914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.