Highest Common Factor of 305, 184, 238 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 305, 184, 238 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 305, 184, 238 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 305, 184, 238 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 305, 184, 238 is 1.

HCF(305, 184, 238) = 1

HCF of 305, 184, 238 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 305, 184, 238 is 1.

Highest Common Factor of 305,184,238 using Euclid's algorithm

Highest Common Factor of 305,184,238 is 1

Step 1: Since 305 > 184, we apply the division lemma to 305 and 184, to get

305 = 184 x 1 + 121

Step 2: Since the reminder 184 ≠ 0, we apply division lemma to 121 and 184, to get

184 = 121 x 1 + 63

Step 3: We consider the new divisor 121 and the new remainder 63, and apply the division lemma to get

121 = 63 x 1 + 58

We consider the new divisor 63 and the new remainder 58,and apply the division lemma to get

63 = 58 x 1 + 5

We consider the new divisor 58 and the new remainder 5,and apply the division lemma to get

58 = 5 x 11 + 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 305 and 184 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(58,5) = HCF(63,58) = HCF(121,63) = HCF(184,121) = HCF(305,184) .

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

Step 1: Since 238 > 1, we apply the division lemma to 238 and 1, to get

238 = 1 x 238 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 238 is 1

Notice that 1 = HCF(238,1) .

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Frequently Asked Questions on HCF of 305, 184, 238 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 305, 184, 238?

Answer: HCF of 305, 184, 238 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 305, 184, 238 using Euclid's Algorithm?

Answer: For arbitrary numbers 305, 184, 238 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.