Highest Common Factor of 238, 380, 321 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 238, 380, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 238, 380, 321 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 238, 380, 321 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 238, 380, 321 is 1.

HCF(238, 380, 321) = 1

HCF of 238, 380, 321 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 238, 380, 321 is 1.

Highest Common Factor of 238,380,321 using Euclid's algorithm

Highest Common Factor of 238,380,321 is 1

Step 1: Since 380 > 238, we apply the division lemma to 380 and 238, to get

380 = 238 x 1 + 142

Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 142 and 238, to get

238 = 142 x 1 + 96

Step 3: We consider the new divisor 142 and the new remainder 96, and apply the division lemma to get

142 = 96 x 1 + 46

We consider the new divisor 96 and the new remainder 46,and apply the division lemma to get

96 = 46 x 2 + 4

We consider the new divisor 46 and the new remainder 4,and apply the division lemma to get

46 = 4 x 11 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 238 and 380 is 2

Notice that 2 = HCF(4,2) = HCF(46,4) = HCF(96,46) = HCF(142,96) = HCF(238,142) = HCF(380,238) .

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

Step 1: Since 321 > 2, we apply the division lemma to 321 and 2, to get

321 = 2 x 160 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 321 is 1

Notice that 1 = HCF(2,1) = HCF(321,2) .

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Frequently Asked Questions on HCF of 238, 380, 321 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 238, 380, 321?

Answer: HCF of 238, 380, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 238, 380, 321 using Euclid's Algorithm?

Answer: For arbitrary numbers 238, 380, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.