Highest Common Factor of 603, 813, 374 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, 813, 374 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 603, 813, 374 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, 813, 374 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, 813, 374 is 1.

HCF(603, 813, 374) = 1

HCF of 603, 813, 374 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, 813, 374 is 1.

Highest Common Factor of 603,813,374 using Euclid's algorithm

Highest Common Factor of 603,813,374 is 1

Step 1: Since 813 > 603, we apply the division lemma to 813 and 603, to get

813 = 603 x 1 + 210

Step 2: Since the reminder 603 ≠ 0, we apply division lemma to 210 and 603, to get

603 = 210 x 2 + 183

Step 3: We consider the new divisor 210 and the new remainder 183, and apply the division lemma to get

210 = 183 x 1 + 27

We consider the new divisor 183 and the new remainder 27,and apply the division lemma to get

183 = 27 x 6 + 21

We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get

27 = 21 x 1 + 6

We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get

21 = 6 x 3 + 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 813 is 3

Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(183,27) = HCF(210,183) = HCF(603,210) = HCF(813,603) .

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

Step 1: Since 374 > 3, we apply the division lemma to 374 and 3, to get

374 = 3 x 124 + 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 374 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(374,3) .

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Frequently Asked Questions on HCF of 603, 813, 374 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, 813, 374?

Answer: HCF of 603, 813, 374 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 603, 813, 374 using Euclid's Algorithm?

Answer: For arbitrary numbers 603, 813, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.