Highest Common Factor of 269, 488 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 269, 488 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 269, 488 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 269, 488 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 269, 488 is 1.

HCF(269, 488) = 1

HCF of 269, 488 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 269, 488 is 1.

Highest Common Factor of 269,488 using Euclid's algorithm

Highest Common Factor of 269,488 is 1

Step 1: Since 488 > 269, we apply the division lemma to 488 and 269, to get

488 = 269 x 1 + 219

Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 219 and 269, to get

269 = 219 x 1 + 50

Step 3: We consider the new divisor 219 and the new remainder 50, and apply the division lemma to get

219 = 50 x 4 + 19

We consider the new divisor 50 and the new remainder 19,and apply the division lemma to get

50 = 19 x 2 + 12

We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get

19 = 12 x 1 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 269 and 488 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(50,19) = HCF(219,50) = HCF(269,219) = HCF(488,269) .

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Frequently Asked Questions on HCF of 269, 488 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 269, 488?

Answer: HCF of 269, 488 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 269, 488 using Euclid's Algorithm?

Answer: For arbitrary numbers 269, 488 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.