Highest Common Factor of 354, 559, 408 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 354, 559, 408 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 559, 408 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 354, 559, 408 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 354, 559, 408 is 1.

HCF(354, 559, 408) = 1

HCF of 354, 559, 408 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 354, 559, 408 is 1.

Highest Common Factor of 354,559,408 using Euclid's algorithm

Highest Common Factor of 354,559,408 is 1

Step 1: Since 559 > 354, we apply the division lemma to 559 and 354, to get

559 = 354 x 1 + 205

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 205 and 354, to get

354 = 205 x 1 + 149

Step 3: We consider the new divisor 205 and the new remainder 149, and apply the division lemma to get

205 = 149 x 1 + 56

We consider the new divisor 149 and the new remainder 56,and apply the division lemma to get

149 = 56 x 2 + 37

We consider the new divisor 56 and the new remainder 37,and apply the division lemma to get

56 = 37 x 1 + 19

We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get

37 = 19 x 1 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 354 and 559 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(56,37) = HCF(149,56) = HCF(205,149) = HCF(354,205) = HCF(559,354) .

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

Step 1: Since 408 > 1, we apply the division lemma to 408 and 1, to get

408 = 1 x 408 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 408 is 1

Notice that 1 = HCF(408,1) .

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Frequently Asked Questions on HCF of 354, 559, 408 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 354, 559, 408?

Answer: HCF of 354, 559, 408 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 559, 408 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 559, 408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.