Highest Common Factor of 748, 765 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, 765 i.e. 17 the largest integer that leaves a remainder zero for all numbers.

HCF of 748, 765 is 17 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, 765 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, 765 is 17.

HCF(748, 765) = 17

HCF of 748, 765 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, 765 is 17.

Highest Common Factor of 748,765 using Euclid's algorithm

Highest Common Factor of 748,765 is 17

Step 1: Since 765 > 748, we apply the division lemma to 765 and 748, to get

765 = 748 x 1 + 17

Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 17 and 748, to get

748 = 17 x 44 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 748 and 765 is 17

Notice that 17 = HCF(748,17) = HCF(765,748) .

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, 765 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, 765?

Answer: HCF of 748, 765 is 17 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 748, 765 using Euclid's Algorithm?

Answer: For arbitrary numbers 748, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.