Highest Common Factor of 829, 313, 80 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 829, 313, 80 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 829, 313, 80 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 829, 313, 80 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 829, 313, 80 is 1.

HCF(829, 313, 80) = 1

HCF of 829, 313, 80 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 829, 313, 80 is 1.

Highest Common Factor of 829,313,80 using Euclid's algorithm

Highest Common Factor of 829,313,80 is 1

Step 1: Since 829 > 313, we apply the division lemma to 829 and 313, to get

829 = 313 x 2 + 203

Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 203 and 313, to get

313 = 203 x 1 + 110

Step 3: We consider the new divisor 203 and the new remainder 110, and apply the division lemma to get

203 = 110 x 1 + 93

We consider the new divisor 110 and the new remainder 93,and apply the division lemma to get

110 = 93 x 1 + 17

We consider the new divisor 93 and the new remainder 17,and apply the division lemma to get

93 = 17 x 5 + 8

We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get

17 = 8 x 2 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 829 and 313 is 1

Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(93,17) = HCF(110,93) = HCF(203,110) = HCF(313,203) = HCF(829,313) .

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

Step 1: Since 80 > 1, we apply the division lemma to 80 and 1, to get

80 = 1 x 80 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 80 is 1

Notice that 1 = HCF(80,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 829, 313, 80 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 829, 313, 80?

Answer: HCF of 829, 313, 80 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 829, 313, 80 using Euclid's Algorithm?

Answer: For arbitrary numbers 829, 313, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.