Highest Common Factor of 448, 8804, 2087 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 448, 8804, 2087 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 448, 8804, 2087 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 448, 8804, 2087 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 448, 8804, 2087 is 1.

HCF(448, 8804, 2087) = 1

HCF of 448, 8804, 2087 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 448, 8804, 2087 is 1.

Highest Common Factor of 448,8804,2087 using Euclid's algorithm

Highest Common Factor of 448,8804,2087 is 1

Step 1: Since 8804 > 448, we apply the division lemma to 8804 and 448, to get

8804 = 448 x 19 + 292

Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 292 and 448, to get

448 = 292 x 1 + 156

Step 3: We consider the new divisor 292 and the new remainder 156, and apply the division lemma to get

292 = 156 x 1 + 136

We consider the new divisor 156 and the new remainder 136,and apply the division lemma to get

156 = 136 x 1 + 20

We consider the new divisor 136 and the new remainder 20,and apply the division lemma to get

136 = 20 x 6 + 16

We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get

20 = 16 x 1 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 448 and 8804 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(136,20) = HCF(156,136) = HCF(292,156) = HCF(448,292) = HCF(8804,448) .

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

Step 1: Since 2087 > 4, we apply the division lemma to 2087 and 4, to get

2087 = 4 x 521 + 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 2087 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(2087,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 448, 8804, 2087 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 448, 8804, 2087?

Answer: HCF of 448, 8804, 2087 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 448, 8804, 2087 using Euclid's Algorithm?

Answer: For arbitrary numbers 448, 8804, 2087 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.