Highest Common Factor of 766, 827, 312 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, 827, 312 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 766, 827, 312 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, 827, 312 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, 827, 312 is 1.

HCF(766, 827, 312) = 1

HCF of 766, 827, 312 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, 827, 312 is 1.

Highest Common Factor of 766,827,312 using Euclid's algorithm

Highest Common Factor of 766,827,312 is 1

Step 1: Since 827 > 766, we apply the division lemma to 827 and 766, to get

827 = 766 x 1 + 61

Step 2: Since the reminder 766 ≠ 0, we apply division lemma to 61 and 766, to get

766 = 61 x 12 + 34

Step 3: We consider the new divisor 61 and the new remainder 34, and apply the division lemma to get

61 = 34 x 1 + 27

We consider the new divisor 34 and the new remainder 27,and apply the division lemma to get

34 = 27 x 1 + 7

We consider the new divisor 27 and the new remainder 7,and apply the division lemma to get

27 = 7 x 3 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 766 and 827 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(27,7) = HCF(34,27) = HCF(61,34) = HCF(766,61) = HCF(827,766) .

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

Step 1: Since 312 > 1, we apply the division lemma to 312 and 1, to get

312 = 1 x 312 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 312 is 1

Notice that 1 = HCF(312,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 766, 827, 312 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, 827, 312?

Answer: HCF of 766, 827, 312 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 766, 827, 312 using Euclid's Algorithm?

Answer: For arbitrary numbers 766, 827, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.