Highest Common Factor of 557, 457, 223 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 557, 457, 223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 557, 457, 223 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 557, 457, 223 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 557, 457, 223 is 1.

HCF(557, 457, 223) = 1

HCF of 557, 457, 223 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 557, 457, 223 is 1.

Highest Common Factor of 557,457,223 using Euclid's algorithm

Highest Common Factor of 557,457,223 is 1

Step 1: Since 557 > 457, we apply the division lemma to 557 and 457, to get

557 = 457 x 1 + 100

Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 100 and 457, to get

457 = 100 x 4 + 57

Step 3: We consider the new divisor 100 and the new remainder 57, and apply the division lemma to get

100 = 57 x 1 + 43

We consider the new divisor 57 and the new remainder 43,and apply the division lemma to get

57 = 43 x 1 + 14

We consider the new divisor 43 and the new remainder 14,and apply the division lemma to get

43 = 14 x 3 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 557 and 457 is 1

Notice that 1 = HCF(14,1) = HCF(43,14) = HCF(57,43) = HCF(100,57) = HCF(457,100) = HCF(557,457) .

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

Step 1: Since 223 > 1, we apply the division lemma to 223 and 1, to get

223 = 1 x 223 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 223 is 1

Notice that 1 = HCF(223,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 557, 457, 223 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 557, 457, 223?

Answer: HCF of 557, 457, 223 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 557, 457, 223 using Euclid's Algorithm?

Answer: For arbitrary numbers 557, 457, 223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.