Highest Common Factor of 178, 307, 354 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 178, 307, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 178, 307, 354 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 178, 307, 354 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 178, 307, 354 is 1.

HCF(178, 307, 354) = 1

HCF of 178, 307, 354 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 178, 307, 354 is 1.

Highest Common Factor of 178,307,354 using Euclid's algorithm

Highest Common Factor of 178,307,354 is 1

Step 1: Since 307 > 178, we apply the division lemma to 307 and 178, to get

307 = 178 x 1 + 129

Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 129 and 178, to get

178 = 129 x 1 + 49

Step 3: We consider the new divisor 129 and the new remainder 49, and apply the division lemma to get

129 = 49 x 2 + 31

We consider the new divisor 49 and the new remainder 31,and apply the division lemma to get

49 = 31 x 1 + 18

We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get

31 = 18 x 1 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 178 and 307 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(49,31) = HCF(129,49) = HCF(178,129) = HCF(307,178) .

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

Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get

354 = 1 x 354 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1

Notice that 1 = HCF(354,1) .

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Frequently Asked Questions on HCF of 178, 307, 354 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 178, 307, 354?

Answer: HCF of 178, 307, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 178, 307, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 178, 307, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.