Highest Common Factor of 554, 585, 343 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, 585, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 554, 585, 343 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, 585, 343 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, 585, 343 is 1.

HCF(554, 585, 343) = 1

HCF of 554, 585, 343 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, 585, 343 is 1.

Highest Common Factor of 554,585,343 using Euclid's algorithm

Highest Common Factor of 554,585,343 is 1

Step 1: Since 585 > 554, we apply the division lemma to 585 and 554, to get

585 = 554 x 1 + 31

Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 31 and 554, to get

554 = 31 x 17 + 27

Step 3: We consider the new divisor 31 and the new remainder 27, and apply the division lemma to get

31 = 27 x 1 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 554 and 585 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(31,27) = HCF(554,31) = HCF(585,554) .

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

Step 1: Since 343 > 1, we apply the division lemma to 343 and 1, to get

343 = 1 x 343 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 343 is 1

Notice that 1 = HCF(343,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 554, 585, 343 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, 585, 343?

Answer: HCF of 554, 585, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 554, 585, 343 using Euclid's Algorithm?

Answer: For arbitrary numbers 554, 585, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.