Highest Common Factor of 723, 988, 263 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 723, 988, 263 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 723, 988, 263 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 723, 988, 263 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 723, 988, 263 is 1.

HCF(723, 988, 263) = 1

HCF of 723, 988, 263 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 723, 988, 263 is 1.

Highest Common Factor of 723,988,263 using Euclid's algorithm

Highest Common Factor of 723,988,263 is 1

Step 1: Since 988 > 723, we apply the division lemma to 988 and 723, to get

988 = 723 x 1 + 265

Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 265 and 723, to get

723 = 265 x 2 + 193

Step 3: We consider the new divisor 265 and the new remainder 193, and apply the division lemma to get

265 = 193 x 1 + 72

We consider the new divisor 193 and the new remainder 72,and apply the division lemma to get

193 = 72 x 2 + 49

We consider the new divisor 72 and the new remainder 49,and apply the division lemma to get

72 = 49 x 1 + 23

We consider the new divisor 49 and the new remainder 23,and apply the division lemma to get

49 = 23 x 2 + 3

We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get

23 = 3 x 7 + 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 723 and 988 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(49,23) = HCF(72,49) = HCF(193,72) = HCF(265,193) = HCF(723,265) = HCF(988,723) .

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

Step 1: Since 263 > 1, we apply the division lemma to 263 and 1, to get

263 = 1 x 263 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 263 is 1

Notice that 1 = HCF(263,1) .

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Frequently Asked Questions on HCF of 723, 988, 263 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 723, 988, 263?

Answer: HCF of 723, 988, 263 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 723, 988, 263 using Euclid's Algorithm?

Answer: For arbitrary numbers 723, 988, 263 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.