Highest Common Factor of 548, 678 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 548, 678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 548, 678 is 2 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 548, 678 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 548, 678 is 2.

HCF(548, 678) = 2

HCF of 548, 678 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 548, 678 is 2.

Highest Common Factor of 548,678 using Euclid's algorithm

Highest Common Factor of 548,678 is 2

Step 1: Since 678 > 548, we apply the division lemma to 678 and 548, to get

678 = 548 x 1 + 130

Step 2: Since the reminder 548 ≠ 0, we apply division lemma to 130 and 548, to get

548 = 130 x 4 + 28

Step 3: We consider the new divisor 130 and the new remainder 28, and apply the division lemma to get

130 = 28 x 4 + 18

We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get

28 = 18 x 1 + 10

We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get

18 = 10 x 1 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 548 and 678 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(130,28) = HCF(548,130) = HCF(678,548) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 548, 678 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 548, 678?

Answer: HCF of 548, 678 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 548, 678 using Euclid's Algorithm?

Answer: For arbitrary numbers 548, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.