Highest Common Factor of 419, 649 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 419, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 649 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 419, 649 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 419, 649 is 1.

HCF(419, 649) = 1

HCF of 419, 649 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 419, 649 is 1.

Highest Common Factor of 419,649 using Euclid's algorithm

Highest Common Factor of 419,649 is 1

Step 1: Since 649 > 419, we apply the division lemma to 649 and 419, to get

649 = 419 x 1 + 230

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 230 and 419, to get

419 = 230 x 1 + 189

Step 3: We consider the new divisor 230 and the new remainder 189, and apply the division lemma to get

230 = 189 x 1 + 41

We consider the new divisor 189 and the new remainder 41,and apply the division lemma to get

189 = 41 x 4 + 25

We consider the new divisor 41 and the new remainder 25,and apply the division lemma to get

41 = 25 x 1 + 16

We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get

25 = 16 x 1 + 9

We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get

16 = 9 x 1 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 1

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 419 and 649 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(41,25) = HCF(189,41) = HCF(230,189) = HCF(419,230) = HCF(649,419) .

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Frequently Asked Questions on HCF of 419, 649 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 419, 649?

Answer: HCF of 419, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 649 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.