Highest Common Factor of 420, 269 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 420, 269 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 269 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 420, 269 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 420, 269 is 1.

HCF(420, 269) = 1

HCF of 420, 269 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 420, 269 is 1.

Highest Common Factor of 420,269 using Euclid's algorithm

Highest Common Factor of 420,269 is 1

Step 1: Since 420 > 269, we apply the division lemma to 420 and 269, to get

420 = 269 x 1 + 151

Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 151 and 269, to get

269 = 151 x 1 + 118

Step 3: We consider the new divisor 151 and the new remainder 118, and apply the division lemma to get

151 = 118 x 1 + 33

We consider the new divisor 118 and the new remainder 33,and apply the division lemma to get

118 = 33 x 3 + 19

We consider the new divisor 33 and the new remainder 19,and apply the division lemma to get

33 = 19 x 1 + 14

We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

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 420 and 269 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(33,19) = HCF(118,33) = HCF(151,118) = HCF(269,151) = HCF(420,269) .

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Frequently Asked Questions on HCF of 420, 269 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 420, 269?

Answer: HCF of 420, 269 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 269 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.