Highest Common Factor of 240, 360, 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 240, 360, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 240, 360, 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 240, 360, 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 240, 360, 209 is 1.

HCF(240, 360, 209) = 1

HCF of 240, 360, 209 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 240, 360, 209 is 1.

Highest Common Factor of 240,360,209 using Euclid's algorithm

Highest Common Factor of 240,360,209 is 1

Step 1: Since 360 > 240, we apply the division lemma to 360 and 240, to get

360 = 240 x 1 + 120

Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 120 and 240, to get

240 = 120 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 120, the HCF of 240 and 360 is 120

Notice that 120 = HCF(240,120) = HCF(360,240) .

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

Step 1: Since 209 > 120, we apply the division lemma to 209 and 120, to get

209 = 120 x 1 + 89

Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 89 and 120, to get

120 = 89 x 1 + 31

Step 3: We consider the new divisor 89 and the new remainder 31, and apply the division lemma to get

89 = 31 x 2 + 27

We consider the new divisor 31 and the new remainder 27,and apply the division lemma to get

31 = 27 x 1 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 120 and 209 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(31,27) = HCF(89,31) = HCF(120,89) = HCF(209,120) .

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Frequently Asked Questions on HCF of 240, 360, 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 240, 360, 209?

Answer: HCF of 240, 360, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 240, 360, 209 using Euclid's Algorithm?

Answer: For arbitrary numbers 240, 360, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.