Highest Common Factor of 103, 168, 203 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 103, 168, 203 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 103, 168, 203 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 103, 168, 203 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 103, 168, 203 is 1.

HCF(103, 168, 203) = 1

HCF of 103, 168, 203 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 103, 168, 203 is 1.

Highest Common Factor of 103,168,203 using Euclid's algorithm

Highest Common Factor of 103,168,203 is 1

Step 1: Since 168 > 103, we apply the division lemma to 168 and 103, to get

168 = 103 x 1 + 65

Step 2: Since the reminder 103 ≠ 0, we apply division lemma to 65 and 103, to get

103 = 65 x 1 + 38

Step 3: We consider the new divisor 65 and the new remainder 38, and apply the division lemma to get

65 = 38 x 1 + 27

We consider the new divisor 38 and the new remainder 27,and apply the division lemma to get

38 = 27 x 1 + 11

We consider the new divisor 27 and the new remainder 11,and apply the division lemma to get

27 = 11 x 2 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 103 and 168 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(27,11) = HCF(38,27) = HCF(65,38) = HCF(103,65) = HCF(168,103) .

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

Step 1: Since 203 > 1, we apply the division lemma to 203 and 1, to get

203 = 1 x 203 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 203 is 1

Notice that 1 = HCF(203,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 103, 168, 203 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 103, 168, 203?

Answer: HCF of 103, 168, 203 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 103, 168, 203 using Euclid's Algorithm?

Answer: For arbitrary numbers 103, 168, 203 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.