Highest Common Factor of 3690, 5744 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 3690, 5744 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 3690, 5744 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 3690, 5744 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 3690, 5744 is 2.

HCF(3690, 5744) = 2

HCF of 3690, 5744 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 3690, 5744 is 2.

Highest Common Factor of 3690,5744 using Euclid's algorithm

Highest Common Factor of 3690,5744 is 2

Step 1: Since 5744 > 3690, we apply the division lemma to 5744 and 3690, to get

5744 = 3690 x 1 + 2054

Step 2: Since the reminder 3690 ≠ 0, we apply division lemma to 2054 and 3690, to get

3690 = 2054 x 1 + 1636

Step 3: We consider the new divisor 2054 and the new remainder 1636, and apply the division lemma to get

2054 = 1636 x 1 + 418

We consider the new divisor 1636 and the new remainder 418,and apply the division lemma to get

1636 = 418 x 3 + 382

We consider the new divisor 418 and the new remainder 382,and apply the division lemma to get

418 = 382 x 1 + 36

We consider the new divisor 382 and the new remainder 36,and apply the division lemma to get

382 = 36 x 10 + 22

We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get

36 = 22 x 1 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3690 and 5744 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(382,36) = HCF(418,382) = HCF(1636,418) = HCF(2054,1636) = HCF(3690,2054) = HCF(5744,3690) .

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Frequently Asked Questions on HCF of 3690, 5744 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 3690, 5744?

Answer: HCF of 3690, 5744 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3690, 5744 using Euclid's Algorithm?

Answer: For arbitrary numbers 3690, 5744 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.