Highest Common Factor of 675, 2028 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 675, 2028 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 2028 is 3 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 675, 2028 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 675, 2028 is 3.

HCF(675, 2028) = 3

HCF of 675, 2028 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 675, 2028 is 3.

Highest Common Factor of 675,2028 using Euclid's algorithm

Highest Common Factor of 675,2028 is 3

Step 1: Since 2028 > 675, we apply the division lemma to 2028 and 675, to get

2028 = 675 x 3 + 3

Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 3 and 675, to get

675 = 3 x 225 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 675 and 2028 is 3

Notice that 3 = HCF(675,3) = HCF(2028,675) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 675, 2028 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 675, 2028?

Answer: HCF of 675, 2028 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 2028 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 2028 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.