Highest Common Factor of 330, 557, 578 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 330, 557, 578 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 330, 557, 578 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 330, 557, 578 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 330, 557, 578 is 1.

HCF(330, 557, 578) = 1

HCF of 330, 557, 578 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 330, 557, 578 is 1.

Highest Common Factor of 330,557,578 using Euclid's algorithm

Highest Common Factor of 330,557,578 is 1

Step 1: Since 557 > 330, we apply the division lemma to 557 and 330, to get

557 = 330 x 1 + 227

Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 227 and 330, to get

330 = 227 x 1 + 103

Step 3: We consider the new divisor 227 and the new remainder 103, and apply the division lemma to get

227 = 103 x 2 + 21

We consider the new divisor 103 and the new remainder 21,and apply the division lemma to get

103 = 21 x 4 + 19

We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get

21 = 19 x 1 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 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 330 and 557 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(103,21) = HCF(227,103) = HCF(330,227) = HCF(557,330) .

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

Step 1: Since 578 > 1, we apply the division lemma to 578 and 1, to get

578 = 1 x 578 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 578 is 1

Notice that 1 = HCF(578,1) .

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Frequently Asked Questions on HCF of 330, 557, 578 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 330, 557, 578?

Answer: HCF of 330, 557, 578 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 330, 557, 578 using Euclid's Algorithm?

Answer: For arbitrary numbers 330, 557, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.