Highest Common Factor of 209, 402 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 209, 402 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 209, 402 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 209, 402 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 209, 402 is 1.

HCF(209, 402) = 1

HCF of 209, 402 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 209, 402 is 1.

Highest Common Factor of 209,402 using Euclid's algorithm

Highest Common Factor of 209,402 is 1

Step 1: Since 402 > 209, we apply the division lemma to 402 and 209, to get

402 = 209 x 1 + 193

Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 193 and 209, to get

209 = 193 x 1 + 16

Step 3: We consider the new divisor 193 and the new remainder 16, and apply the division lemma to get

193 = 16 x 12 + 1

We consider the new divisor 16 and the new remainder 1, and apply the division lemma to get

16 = 1 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 209 and 402 is 1

Notice that 1 = HCF(16,1) = HCF(193,16) = HCF(209,193) = HCF(402,209) .

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Frequently Asked Questions on HCF of 209, 402 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 209, 402?

Answer: HCF of 209, 402 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 209, 402 using Euclid's Algorithm?

Answer: For arbitrary numbers 209, 402 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.