Highest Common Factor of 727, 8976 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 727, 8976 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 727, 8976 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 727, 8976 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 727, 8976 is 1.

HCF(727, 8976) = 1

HCF of 727, 8976 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 727, 8976 is 1.

Highest Common Factor of 727,8976 using Euclid's algorithm

Highest Common Factor of 727,8976 is 1

Step 1: Since 8976 > 727, we apply the division lemma to 8976 and 727, to get

8976 = 727 x 12 + 252

Step 2: Since the reminder 727 ≠ 0, we apply division lemma to 252 and 727, to get

727 = 252 x 2 + 223

Step 3: We consider the new divisor 252 and the new remainder 223, and apply the division lemma to get

252 = 223 x 1 + 29

We consider the new divisor 223 and the new remainder 29,and apply the division lemma to get

223 = 29 x 7 + 20

We consider the new divisor 29 and the new remainder 20,and apply the division lemma to get

29 = 20 x 1 + 9

We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get

20 = 9 x 2 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 727 and 8976 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(29,20) = HCF(223,29) = HCF(252,223) = HCF(727,252) = HCF(8976,727) .

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Frequently Asked Questions on HCF of 727, 8976 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 727, 8976?

Answer: HCF of 727, 8976 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 727, 8976 using Euclid's Algorithm?

Answer: For arbitrary numbers 727, 8976 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.