Highest Common Factor of 908, 315, 221 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 908, 315, 221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 908, 315, 221 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 908, 315, 221 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 908, 315, 221 is 1.

HCF(908, 315, 221) = 1

HCF of 908, 315, 221 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 908, 315, 221 is 1.

Highest Common Factor of 908,315,221 using Euclid's algorithm

Highest Common Factor of 908,315,221 is 1

Step 1: Since 908 > 315, we apply the division lemma to 908 and 315, to get

908 = 315 x 2 + 278

Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 278 and 315, to get

315 = 278 x 1 + 37

Step 3: We consider the new divisor 278 and the new remainder 37, and apply the division lemma to get

278 = 37 x 7 + 19

We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get

37 = 19 x 1 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 908 and 315 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(278,37) = HCF(315,278) = HCF(908,315) .

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

Step 1: Since 221 > 1, we apply the division lemma to 221 and 1, to get

221 = 1 x 221 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 221 is 1

Notice that 1 = HCF(221,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 908, 315, 221 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 908, 315, 221?

Answer: HCF of 908, 315, 221 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 908, 315, 221 using Euclid's Algorithm?

Answer: For arbitrary numbers 908, 315, 221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.