Highest Common Factor of 603, 912, 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 603, 912, 578 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 603, 912, 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 603, 912, 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 603, 912, 578 is 1.

HCF(603, 912, 578) = 1

HCF of 603, 912, 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 603, 912, 578 is 1.

Highest Common Factor of 603,912,578 using Euclid's algorithm

Highest Common Factor of 603,912,578 is 1

Step 1: Since 912 > 603, we apply the division lemma to 912 and 603, to get

912 = 603 x 1 + 309

Step 2: Since the reminder 603 ≠ 0, we apply division lemma to 309 and 603, to get

603 = 309 x 1 + 294

Step 3: We consider the new divisor 309 and the new remainder 294, and apply the division lemma to get

309 = 294 x 1 + 15

We consider the new divisor 294 and the new remainder 15,and apply the division lemma to get

294 = 15 x 19 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 603 and 912 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(294,15) = HCF(309,294) = HCF(603,309) = HCF(912,603) .

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

Step 1: Since 578 > 3, we apply the division lemma to 578 and 3, to get

578 = 3 x 192 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 578 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(578,3) .

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Frequently Asked Questions on HCF of 603, 912, 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 603, 912, 578?

Answer: HCF of 603, 912, 578 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 603, 912, 578 using Euclid's Algorithm?

Answer: For arbitrary numbers 603, 912, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.