Highest Common Factor of 127, 462, 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 127, 462, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 127, 462, 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 127, 462, 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 127, 462, 209 is 1.

HCF(127, 462, 209) = 1

HCF of 127, 462, 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 127, 462, 209 is 1.

Highest Common Factor of 127,462,209 using Euclid's algorithm

Highest Common Factor of 127,462,209 is 1

Step 1: Since 462 > 127, we apply the division lemma to 462 and 127, to get

462 = 127 x 3 + 81

Step 2: Since the reminder 127 ≠ 0, we apply division lemma to 81 and 127, to get

127 = 81 x 1 + 46

Step 3: We consider the new divisor 81 and the new remainder 46, and apply the division lemma to get

81 = 46 x 1 + 35

We consider the new divisor 46 and the new remainder 35,and apply the division lemma to get

46 = 35 x 1 + 11

We consider the new divisor 35 and the new remainder 11,and apply the division lemma to get

35 = 11 x 3 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 127 and 462 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(35,11) = HCF(46,35) = HCF(81,46) = HCF(127,81) = HCF(462,127) .

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

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

209 = 1 x 209 + 0

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

Notice that 1 = HCF(209,1) .

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Frequently Asked Questions on HCF of 127, 462, 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 127, 462, 209?

Answer: HCF of 127, 462, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 127, 462, 209 using Euclid's Algorithm?

Answer: For arbitrary numbers 127, 462, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.