Highest Common Factor of 135, 381, 304 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 135, 381, 304 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 135, 381, 304 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 135, 381, 304 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 135, 381, 304 is 1.

HCF(135, 381, 304) = 1

HCF of 135, 381, 304 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 135, 381, 304 is 1.

Highest Common Factor of 135,381,304 using Euclid's algorithm

Highest Common Factor of 135,381,304 is 1

Step 1: Since 381 > 135, we apply the division lemma to 381 and 135, to get

381 = 135 x 2 + 111

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 111 and 135, to get

135 = 111 x 1 + 24

Step 3: We consider the new divisor 111 and the new remainder 24, and apply the division lemma to get

111 = 24 x 4 + 15

We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 135 and 381 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(111,24) = HCF(135,111) = HCF(381,135) .

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

Step 1: Since 304 > 3, we apply the division lemma to 304 and 3, to get

304 = 3 x 101 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 304 is 1

Notice that 1 = HCF(3,1) = HCF(304,3) .

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Frequently Asked Questions on HCF of 135, 381, 304 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 135, 381, 304?

Answer: HCF of 135, 381, 304 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 135, 381, 304 using Euclid's Algorithm?

Answer: For arbitrary numbers 135, 381, 304 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.