Highest Common Factor of 374, 583, 585 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 374, 583, 585 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 374, 583, 585 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 374, 583, 585 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 374, 583, 585 is 1.

HCF(374, 583, 585) = 1

HCF of 374, 583, 585 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 374, 583, 585 is 1.

Highest Common Factor of 374,583,585 using Euclid's algorithm

Highest Common Factor of 374,583,585 is 1

Step 1: Since 583 > 374, we apply the division lemma to 583 and 374, to get

583 = 374 x 1 + 209

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 209 and 374, to get

374 = 209 x 1 + 165

Step 3: We consider the new divisor 209 and the new remainder 165, and apply the division lemma to get

209 = 165 x 1 + 44

We consider the new divisor 165 and the new remainder 44,and apply the division lemma to get

165 = 44 x 3 + 33

We consider the new divisor 44 and the new remainder 33,and apply the division lemma to get

44 = 33 x 1 + 11

We consider the new divisor 33 and the new remainder 11,and apply the division lemma to get

33 = 11 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 374 and 583 is 11

Notice that 11 = HCF(33,11) = HCF(44,33) = HCF(165,44) = HCF(209,165) = HCF(374,209) = HCF(583,374) .

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

Step 1: Since 585 > 11, we apply the division lemma to 585 and 11, to get

585 = 11 x 53 + 2

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 2 and 11, to get

11 = 2 x 5 + 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 11 and 585 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(585,11) .

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Frequently Asked Questions on HCF of 374, 583, 585 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 374, 583, 585?

Answer: HCF of 374, 583, 585 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 374, 583, 585 using Euclid's Algorithm?

Answer: For arbitrary numbers 374, 583, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.