Highest Common Factor of 723, 914, 77, 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 723, 914, 77, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 723, 914, 77, 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 723, 914, 77, 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 723, 914, 77, 343 is 1.

HCF(723, 914, 77, 343) = 1

HCF of 723, 914, 77, 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 723, 914, 77, 343 is 1.

Highest Common Factor of 723,914,77,343 using Euclid's algorithm

Highest Common Factor of 723,914,77,343 is 1

Step 1: Since 914 > 723, we apply the division lemma to 914 and 723, to get

914 = 723 x 1 + 191

Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 191 and 723, to get

723 = 191 x 3 + 150

Step 3: We consider the new divisor 191 and the new remainder 150, and apply the division lemma to get

191 = 150 x 1 + 41

We consider the new divisor 150 and the new remainder 41,and apply the division lemma to get

150 = 41 x 3 + 27

We consider the new divisor 41 and the new remainder 27,and apply the division lemma to get

41 = 27 x 1 + 14

We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get

27 = 14 x 1 + 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 723 and 914 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(41,27) = HCF(150,41) = HCF(191,150) = HCF(723,191) = HCF(914,723) .

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

Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get

77 = 1 x 77 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1

Notice that 1 = HCF(77,1) .

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

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

343 = 1 x 343 + 0

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

Notice that 1 = HCF(343,1) .

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Frequently Asked Questions on HCF of 723, 914, 77, 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 723, 914, 77, 343?

Answer: HCF of 723, 914, 77, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 723, 914, 77, 343 using Euclid's Algorithm?

Answer: For arbitrary numbers 723, 914, 77, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.