Highest Common Factor of 382, 704, 404 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 382, 704, 404 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 382, 704, 404 is 2 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 382, 704, 404 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 382, 704, 404 is 2.

HCF(382, 704, 404) = 2

HCF of 382, 704, 404 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 382, 704, 404 is 2.

Highest Common Factor of 382,704,404 using Euclid's algorithm

Highest Common Factor of 382,704,404 is 2

Step 1: Since 704 > 382, we apply the division lemma to 704 and 382, to get

704 = 382 x 1 + 322

Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 322 and 382, to get

382 = 322 x 1 + 60

Step 3: We consider the new divisor 322 and the new remainder 60, and apply the division lemma to get

322 = 60 x 5 + 22

We consider the new divisor 60 and the new remainder 22,and apply the division lemma to get

60 = 22 x 2 + 16

We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get

22 = 16 x 1 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 382 and 704 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(60,22) = HCF(322,60) = HCF(382,322) = HCF(704,382) .

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

Step 1: Since 404 > 2, we apply the division lemma to 404 and 2, to get

404 = 2 x 202 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 404 is 2

Notice that 2 = HCF(404,2) .

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Frequently Asked Questions on HCF of 382, 704, 404 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 382, 704, 404?

Answer: HCF of 382, 704, 404 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 382, 704, 404 using Euclid's Algorithm?

Answer: For arbitrary numbers 382, 704, 404 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.