Highest Common Factor of 409, 639 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 409, 639 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 409, 639 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 409, 639 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 409, 639 is 1.

HCF(409, 639) = 1

HCF of 409, 639 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 409, 639 is 1.

Highest Common Factor of 409,639 using Euclid's algorithm

Highest Common Factor of 409,639 is 1

Step 1: Since 639 > 409, we apply the division lemma to 639 and 409, to get

639 = 409 x 1 + 230

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 230 and 409, to get

409 = 230 x 1 + 179

Step 3: We consider the new divisor 230 and the new remainder 179, and apply the division lemma to get

230 = 179 x 1 + 51

We consider the new divisor 179 and the new remainder 51,and apply the division lemma to get

179 = 51 x 3 + 26

We consider the new divisor 51 and the new remainder 26,and apply the division lemma to get

51 = 26 x 1 + 25

We consider the new divisor 26 and the new remainder 25,and apply the division lemma to get

26 = 25 x 1 + 1

We consider the new divisor 25 and the new remainder 1,and apply the division lemma to get

25 = 1 x 25 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 409 and 639 is 1

Notice that 1 = HCF(25,1) = HCF(26,25) = HCF(51,26) = HCF(179,51) = HCF(230,179) = HCF(409,230) = HCF(639,409) .

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Frequently Asked Questions on HCF of 409, 639 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 409, 639?

Answer: HCF of 409, 639 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 409, 639 using Euclid's Algorithm?

Answer: For arbitrary numbers 409, 639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.