Highest Common Factor of 1649, 5640 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 1649, 5640 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1649, 5640 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 1649, 5640 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 1649, 5640 is 1.

HCF(1649, 5640) = 1

HCF of 1649, 5640 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 1649, 5640 is 1.

Highest Common Factor of 1649,5640 using Euclid's algorithm

Highest Common Factor of 1649,5640 is 1

Step 1: Since 5640 > 1649, we apply the division lemma to 5640 and 1649, to get

5640 = 1649 x 3 + 693

Step 2: Since the reminder 1649 ≠ 0, we apply division lemma to 693 and 1649, to get

1649 = 693 x 2 + 263

Step 3: We consider the new divisor 693 and the new remainder 263, and apply the division lemma to get

693 = 263 x 2 + 167

We consider the new divisor 263 and the new remainder 167,and apply the division lemma to get

263 = 167 x 1 + 96

We consider the new divisor 167 and the new remainder 96,and apply the division lemma to get

167 = 96 x 1 + 71

We consider the new divisor 96 and the new remainder 71,and apply the division lemma to get

96 = 71 x 1 + 25

We consider the new divisor 71 and the new remainder 25,and apply the division lemma to get

71 = 25 x 2 + 21

We consider the new divisor 25 and the new remainder 21,and apply the division lemma to get

25 = 21 x 1 + 4

We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get

21 = 4 x 5 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1649 and 5640 is 1

Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(25,21) = HCF(71,25) = HCF(96,71) = HCF(167,96) = HCF(263,167) = HCF(693,263) = HCF(1649,693) = HCF(5640,1649) .

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Frequently Asked Questions on HCF of 1649, 5640 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 1649, 5640?

Answer: HCF of 1649, 5640 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1649, 5640 using Euclid's Algorithm?

Answer: For arbitrary numbers 1649, 5640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.