Highest Common Factor of 239, 372, 71 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 239, 372, 71 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 239, 372, 71 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 239, 372, 71 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 239, 372, 71 is 1.

HCF(239, 372, 71) = 1

HCF of 239, 372, 71 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 239, 372, 71 is 1.

Highest Common Factor of 239,372,71 using Euclid's algorithm

Highest Common Factor of 239,372,71 is 1

Step 1: Since 372 > 239, we apply the division lemma to 372 and 239, to get

372 = 239 x 1 + 133

Step 2: Since the reminder 239 ≠ 0, we apply division lemma to 133 and 239, to get

239 = 133 x 1 + 106

Step 3: We consider the new divisor 133 and the new remainder 106, and apply the division lemma to get

133 = 106 x 1 + 27

We consider the new divisor 106 and the new remainder 27,and apply the division lemma to get

106 = 27 x 3 + 25

We consider the new divisor 27 and the new remainder 25,and apply the division lemma to get

27 = 25 x 1 + 2

We consider the new divisor 25 and the new remainder 2,and apply the division lemma to get

25 = 2 x 12 + 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 239 and 372 is 1

Notice that 1 = HCF(2,1) = HCF(25,2) = HCF(27,25) = HCF(106,27) = HCF(133,106) = HCF(239,133) = HCF(372,239) .

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

Step 1: Since 71 > 1, we apply the division lemma to 71 and 1, to get

71 = 1 x 71 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 71 is 1

Notice that 1 = HCF(71,1) .

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Frequently Asked Questions on HCF of 239, 372, 71 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 239, 372, 71?

Answer: HCF of 239, 372, 71 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 239, 372, 71 using Euclid's Algorithm?

Answer: For arbitrary numbers 239, 372, 71 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.