Highest Common Factor of 269, 750, 223 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, 750, 223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 269, 750, 223 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, 750, 223 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, 750, 223 is 1.

HCF(269, 750, 223) = 1

HCF of 269, 750, 223 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, 750, 223 is 1.

Highest Common Factor of 269,750,223 using Euclid's algorithm

Highest Common Factor of 269,750,223 is 1

Step 1: Since 750 > 269, we apply the division lemma to 750 and 269, to get

750 = 269 x 2 + 212

Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 212 and 269, to get

269 = 212 x 1 + 57

Step 3: We consider the new divisor 212 and the new remainder 57, and apply the division lemma to get

212 = 57 x 3 + 41

We consider the new divisor 57 and the new remainder 41,and apply the division lemma to get

57 = 41 x 1 + 16

We consider the new divisor 41 and the new remainder 16,and apply the division lemma to get

41 = 16 x 2 + 9

We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get

16 = 9 x 1 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 750 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(41,16) = HCF(57,41) = HCF(212,57) = HCF(269,212) = HCF(750,269) .

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

Step 1: Since 223 > 1, we apply the division lemma to 223 and 1, to get

223 = 1 x 223 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 223 is 1

Notice that 1 = HCF(223,1) .

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Frequently Asked Questions on HCF of 269, 750, 223 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, 750, 223?

Answer: HCF of 269, 750, 223 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 269, 750, 223 using Euclid's Algorithm?

Answer: For arbitrary numbers 269, 750, 223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.