Highest Common Factor of 272, 709, 348 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 272, 709, 348 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 272, 709, 348 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 272, 709, 348 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 272, 709, 348 is 1.

HCF(272, 709, 348) = 1

HCF of 272, 709, 348 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 272, 709, 348 is 1.

Highest Common Factor of 272,709,348 using Euclid's algorithm

Highest Common Factor of 272,709,348 is 1

Step 1: Since 709 > 272, we apply the division lemma to 709 and 272, to get

709 = 272 x 2 + 165

Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 165 and 272, to get

272 = 165 x 1 + 107

Step 3: We consider the new divisor 165 and the new remainder 107, and apply the division lemma to get

165 = 107 x 1 + 58

We consider the new divisor 107 and the new remainder 58,and apply the division lemma to get

107 = 58 x 1 + 49

We consider the new divisor 58 and the new remainder 49,and apply the division lemma to get

58 = 49 x 1 + 9

We consider the new divisor 49 and the new remainder 9,and apply the division lemma to get

49 = 9 x 5 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 272 and 709 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(49,9) = HCF(58,49) = HCF(107,58) = HCF(165,107) = HCF(272,165) = HCF(709,272) .

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

Step 1: Since 348 > 1, we apply the division lemma to 348 and 1, to get

348 = 1 x 348 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 348 is 1

Notice that 1 = HCF(348,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 272, 709, 348 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 272, 709, 348?

Answer: HCF of 272, 709, 348 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 272, 709, 348 using Euclid's Algorithm?

Answer: For arbitrary numbers 272, 709, 348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.