Highest Common Factor of 509, 420 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 509, 420 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 509, 420 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 509, 420 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 509, 420 is 1.

HCF(509, 420) = 1

HCF of 509, 420 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 509, 420 is 1.

Highest Common Factor of 509,420 using Euclid's algorithm

Highest Common Factor of 509,420 is 1

Step 1: Since 509 > 420, we apply the division lemma to 509 and 420, to get

509 = 420 x 1 + 89

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 89 and 420, to get

420 = 89 x 4 + 64

Step 3: We consider the new divisor 89 and the new remainder 64, and apply the division lemma to get

89 = 64 x 1 + 25

We consider the new divisor 64 and the new remainder 25,and apply the division lemma to get

64 = 25 x 2 + 14

We consider the new divisor 25 and the new remainder 14,and apply the division lemma to get

25 = 14 x 1 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 509 and 420 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(64,25) = HCF(89,64) = HCF(420,89) = HCF(509,420) .

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Frequently Asked Questions on HCF of 509, 420 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 509, 420?

Answer: HCF of 509, 420 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 509, 420 using Euclid's Algorithm?

Answer: For arbitrary numbers 509, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.