Highest Common Factor of 304, 189, 270 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 304, 189, 270 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 304, 189, 270 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 304, 189, 270 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 304, 189, 270 is 1.

HCF(304, 189, 270) = 1

HCF of 304, 189, 270 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 304, 189, 270 is 1.

Highest Common Factor of 304,189,270 using Euclid's algorithm

Highest Common Factor of 304,189,270 is 1

Step 1: Since 304 > 189, we apply the division lemma to 304 and 189, to get

304 = 189 x 1 + 115

Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 115 and 189, to get

189 = 115 x 1 + 74

Step 3: We consider the new divisor 115 and the new remainder 74, and apply the division lemma to get

115 = 74 x 1 + 41

We consider the new divisor 74 and the new remainder 41,and apply the division lemma to get

74 = 41 x 1 + 33

We consider the new divisor 41 and the new remainder 33,and apply the division lemma to get

41 = 33 x 1 + 8

We consider the new divisor 33 and the new remainder 8,and apply the division lemma to get

33 = 8 x 4 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 304 and 189 is 1

Notice that 1 = HCF(8,1) = HCF(33,8) = HCF(41,33) = HCF(74,41) = HCF(115,74) = HCF(189,115) = HCF(304,189) .

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

Step 1: Since 270 > 1, we apply the division lemma to 270 and 1, to get

270 = 1 x 270 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 270 is 1

Notice that 1 = HCF(270,1) .

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Frequently Asked Questions on HCF of 304, 189, 270 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 304, 189, 270?

Answer: HCF of 304, 189, 270 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 304, 189, 270 using Euclid's Algorithm?

Answer: For arbitrary numbers 304, 189, 270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.