Highest Common Factor of 554, 903 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 554, 903 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 554, 903 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 554, 903 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 554, 903 is 1.

HCF(554, 903) = 1

HCF of 554, 903 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 554, 903 is 1.

Highest Common Factor of 554,903 using Euclid's algorithm

Highest Common Factor of 554,903 is 1

Step 1: Since 903 > 554, we apply the division lemma to 903 and 554, to get

903 = 554 x 1 + 349

Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 349 and 554, to get

554 = 349 x 1 + 205

Step 3: We consider the new divisor 349 and the new remainder 205, and apply the division lemma to get

349 = 205 x 1 + 144

We consider the new divisor 205 and the new remainder 144,and apply the division lemma to get

205 = 144 x 1 + 61

We consider the new divisor 144 and the new remainder 61,and apply the division lemma to get

144 = 61 x 2 + 22

We consider the new divisor 61 and the new remainder 22,and apply the division lemma to get

61 = 22 x 2 + 17

We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get

22 = 17 x 1 + 5

We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get

17 = 5 x 3 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 554 and 903 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(61,22) = HCF(144,61) = HCF(205,144) = HCF(349,205) = HCF(554,349) = HCF(903,554) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 554, 903 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 554, 903?

Answer: HCF of 554, 903 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 554, 903 using Euclid's Algorithm?

Answer: For arbitrary numbers 554, 903 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.