Highest Common Factor of 820, 452, 319 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 820, 452, 319 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 820, 452, 319 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 820, 452, 319 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 820, 452, 319 is 1.

HCF(820, 452, 319) = 1

HCF of 820, 452, 319 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 820, 452, 319 is 1.

Highest Common Factor of 820,452,319 using Euclid's algorithm

Highest Common Factor of 820,452,319 is 1

Step 1: Since 820 > 452, we apply the division lemma to 820 and 452, to get

820 = 452 x 1 + 368

Step 2: Since the reminder 452 ≠ 0, we apply division lemma to 368 and 452, to get

452 = 368 x 1 + 84

Step 3: We consider the new divisor 368 and the new remainder 84, and apply the division lemma to get

368 = 84 x 4 + 32

We consider the new divisor 84 and the new remainder 32,and apply the division lemma to get

84 = 32 x 2 + 20

We consider the new divisor 32 and the new remainder 20,and apply the division lemma to get

32 = 20 x 1 + 12

We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get

20 = 12 x 1 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 820 and 452 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(84,32) = HCF(368,84) = HCF(452,368) = HCF(820,452) .

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

Step 1: Since 319 > 4, we apply the division lemma to 319 and 4, to get

319 = 4 x 79 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 319 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(319,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 820, 452, 319 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 820, 452, 319?

Answer: HCF of 820, 452, 319 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 820, 452, 319 using Euclid's Algorithm?

Answer: For arbitrary numbers 820, 452, 319 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.