Highest Common Factor of 748, 272, 767 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 748, 272, 767 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 748, 272, 767 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 748, 272, 767 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 748, 272, 767 is 1.

HCF(748, 272, 767) = 1

HCF of 748, 272, 767 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 748, 272, 767 is 1.

Highest Common Factor of 748,272,767 using Euclid's algorithm

Highest Common Factor of 748,272,767 is 1

Step 1: Since 748 > 272, we apply the division lemma to 748 and 272, to get

748 = 272 x 2 + 204

Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 204 and 272, to get

272 = 204 x 1 + 68

Step 3: We consider the new divisor 204 and the new remainder 68, and apply the division lemma to get

204 = 68 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 68, the HCF of 748 and 272 is 68

Notice that 68 = HCF(204,68) = HCF(272,204) = HCF(748,272) .

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

Step 1: Since 767 > 68, we apply the division lemma to 767 and 68, to get

767 = 68 x 11 + 19

Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 19 and 68, to get

68 = 19 x 3 + 11

Step 3: We consider the new divisor 19 and the new remainder 11, and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 68 and 767 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(68,19) = HCF(767,68) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 748, 272, 767 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 748, 272, 767?

Answer: HCF of 748, 272, 767 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 748, 272, 767 using Euclid's Algorithm?

Answer: For arbitrary numbers 748, 272, 767 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.