Highest Common Factor of 766, 2774, 8509 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 766, 2774, 8509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 766, 2774, 8509 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 766, 2774, 8509 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 766, 2774, 8509 is 1.

HCF(766, 2774, 8509) = 1

HCF of 766, 2774, 8509 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 766, 2774, 8509 is 1.

Highest Common Factor of 766,2774,8509 using Euclid's algorithm

Highest Common Factor of 766,2774,8509 is 1

Step 1: Since 2774 > 766, we apply the division lemma to 2774 and 766, to get

2774 = 766 x 3 + 476

Step 2: Since the reminder 766 ≠ 0, we apply division lemma to 476 and 766, to get

766 = 476 x 1 + 290

Step 3: We consider the new divisor 476 and the new remainder 290, and apply the division lemma to get

476 = 290 x 1 + 186

We consider the new divisor 290 and the new remainder 186,and apply the division lemma to get

290 = 186 x 1 + 104

We consider the new divisor 186 and the new remainder 104,and apply the division lemma to get

186 = 104 x 1 + 82

We consider the new divisor 104 and the new remainder 82,and apply the division lemma to get

104 = 82 x 1 + 22

We consider the new divisor 82 and the new remainder 22,and apply the division lemma to get

82 = 22 x 3 + 16

We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get

22 = 16 x 1 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 766 and 2774 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(82,22) = HCF(104,82) = HCF(186,104) = HCF(290,186) = HCF(476,290) = HCF(766,476) = HCF(2774,766) .

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

Step 1: Since 8509 > 2, we apply the division lemma to 8509 and 2, to get

8509 = 2 x 4254 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 8509 is 1

Notice that 1 = HCF(2,1) = HCF(8509,2) .

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Frequently Asked Questions on HCF of 766, 2774, 8509 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 766, 2774, 8509?

Answer: HCF of 766, 2774, 8509 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 766, 2774, 8509 using Euclid's Algorithm?

Answer: For arbitrary numbers 766, 2774, 8509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.