Highest Common Factor of 905, 361, 20 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 905, 361, 20 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 905, 361, 20 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 905, 361, 20 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 905, 361, 20 is 1.

HCF(905, 361, 20) = 1

HCF of 905, 361, 20 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 905, 361, 20 is 1.

Highest Common Factor of 905,361,20 using Euclid's algorithm

Highest Common Factor of 905,361,20 is 1

Step 1: Since 905 > 361, we apply the division lemma to 905 and 361, to get

905 = 361 x 2 + 183

Step 2: Since the reminder 361 ≠ 0, we apply division lemma to 183 and 361, to get

361 = 183 x 1 + 178

Step 3: We consider the new divisor 183 and the new remainder 178, and apply the division lemma to get

183 = 178 x 1 + 5

We consider the new divisor 178 and the new remainder 5,and apply the division lemma to get

178 = 5 x 35 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 905 and 361 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(178,5) = HCF(183,178) = HCF(361,183) = HCF(905,361) .

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

Step 1: Since 20 > 1, we apply the division lemma to 20 and 1, to get

20 = 1 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20 is 1

Notice that 1 = HCF(20,1) .

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Frequently Asked Questions on HCF of 905, 361, 20 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 905, 361, 20?

Answer: HCF of 905, 361, 20 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 905, 361, 20 using Euclid's Algorithm?

Answer: For arbitrary numbers 905, 361, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.