Highest Common Factor of 331, 545, 654 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 331, 545, 654 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 331, 545, 654 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 331, 545, 654 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 331, 545, 654 is 1.

HCF(331, 545, 654) = 1

HCF of 331, 545, 654 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 331, 545, 654 is 1.

Highest Common Factor of 331,545,654 using Euclid's algorithm

Highest Common Factor of 331,545,654 is 1

Step 1: Since 545 > 331, we apply the division lemma to 545 and 331, to get

545 = 331 x 1 + 214

Step 2: Since the reminder 331 ≠ 0, we apply division lemma to 214 and 331, to get

331 = 214 x 1 + 117

Step 3: We consider the new divisor 214 and the new remainder 117, and apply the division lemma to get

214 = 117 x 1 + 97

We consider the new divisor 117 and the new remainder 97,and apply the division lemma to get

117 = 97 x 1 + 20

We consider the new divisor 97 and the new remainder 20,and apply the division lemma to get

97 = 20 x 4 + 17

We consider the new divisor 20 and the new remainder 17,and apply the division lemma to get

20 = 17 x 1 + 3

We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get

17 = 3 x 5 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 331 and 545 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(20,17) = HCF(97,20) = HCF(117,97) = HCF(214,117) = HCF(331,214) = HCF(545,331) .

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

Step 1: Since 654 > 1, we apply the division lemma to 654 and 1, to get

654 = 1 x 654 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 654 is 1

Notice that 1 = HCF(654,1) .

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Frequently Asked Questions on HCF of 331, 545, 654 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 331, 545, 654?

Answer: HCF of 331, 545, 654 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 331, 545, 654 using Euclid's Algorithm?

Answer: For arbitrary numbers 331, 545, 654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.