Highest Common Factor of 505, 330, 209 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 505, 330, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 330, 209 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 505, 330, 209 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 505, 330, 209 is 1.

HCF(505, 330, 209) = 1

HCF of 505, 330, 209 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 505, 330, 209 is 1.

Highest Common Factor of 505,330,209 using Euclid's algorithm

Highest Common Factor of 505,330,209 is 1

Step 1: Since 505 > 330, we apply the division lemma to 505 and 330, to get

505 = 330 x 1 + 175

Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 175 and 330, to get

330 = 175 x 1 + 155

Step 3: We consider the new divisor 175 and the new remainder 155, and apply the division lemma to get

175 = 155 x 1 + 20

We consider the new divisor 155 and the new remainder 20,and apply the division lemma to get

155 = 20 x 7 + 15

We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get

20 = 15 x 1 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 505 and 330 is 5

Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(155,20) = HCF(175,155) = HCF(330,175) = HCF(505,330) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 209 > 5, we apply the division lemma to 209 and 5, to get

209 = 5 x 41 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: 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 5 and 209 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(209,5) .

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Frequently Asked Questions on HCF of 505, 330, 209 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 505, 330, 209?

Answer: HCF of 505, 330, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 330, 209 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 330, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.