Highest Common Factor of 673, 178, 329 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 673, 178, 329 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 673, 178, 329 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 673, 178, 329 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 673, 178, 329 is 1.

HCF(673, 178, 329) = 1

HCF of 673, 178, 329 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 673, 178, 329 is 1.

Highest Common Factor of 673,178,329 using Euclid's algorithm

Highest Common Factor of 673,178,329 is 1

Step 1: Since 673 > 178, we apply the division lemma to 673 and 178, to get

673 = 178 x 3 + 139

Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 139 and 178, to get

178 = 139 x 1 + 39

Step 3: We consider the new divisor 139 and the new remainder 39, and apply the division lemma to get

139 = 39 x 3 + 22

We consider the new divisor 39 and the new remainder 22,and apply the division lemma to get

39 = 22 x 1 + 17

We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get

22 = 17 x 1 + 5

We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get

17 = 5 x 3 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 673 and 178 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(39,22) = HCF(139,39) = HCF(178,139) = HCF(673,178) .

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

Step 1: Since 329 > 1, we apply the division lemma to 329 and 1, to get

329 = 1 x 329 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 329 is 1

Notice that 1 = HCF(329,1) .

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Frequently Asked Questions on HCF of 673, 178, 329 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 673, 178, 329?

Answer: HCF of 673, 178, 329 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 673, 178, 329 using Euclid's Algorithm?

Answer: For arbitrary numbers 673, 178, 329 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.