Highest Common Factor of 428, 239, 768 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 428, 239, 768 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 428, 239, 768 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 428, 239, 768 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 428, 239, 768 is 1.

HCF(428, 239, 768) = 1

HCF of 428, 239, 768 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 428, 239, 768 is 1.

Highest Common Factor of 428,239,768 using Euclid's algorithm

Highest Common Factor of 428,239,768 is 1

Step 1: Since 428 > 239, we apply the division lemma to 428 and 239, to get

428 = 239 x 1 + 189

Step 2: Since the reminder 239 ≠ 0, we apply division lemma to 189 and 239, to get

239 = 189 x 1 + 50

Step 3: We consider the new divisor 189 and the new remainder 50, and apply the division lemma to get

189 = 50 x 3 + 39

We consider the new divisor 50 and the new remainder 39,and apply the division lemma to get

50 = 39 x 1 + 11

We consider the new divisor 39 and the new remainder 11,and apply the division lemma to get

39 = 11 x 3 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 428 and 239 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(39,11) = HCF(50,39) = HCF(189,50) = HCF(239,189) = HCF(428,239) .

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

Step 1: Since 768 > 1, we apply the division lemma to 768 and 1, to get

768 = 1 x 768 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 768 is 1

Notice that 1 = HCF(768,1) .

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Frequently Asked Questions on HCF of 428, 239, 768 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 428, 239, 768?

Answer: HCF of 428, 239, 768 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 428, 239, 768 using Euclid's Algorithm?

Answer: For arbitrary numbers 428, 239, 768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.