Highest Common Factor of 301, 823, 200 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 301, 823, 200 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 301, 823, 200 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 301, 823, 200 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 301, 823, 200 is 1.

HCF(301, 823, 200) = 1

HCF of 301, 823, 200 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 301, 823, 200 is 1.

Highest Common Factor of 301,823,200 using Euclid's algorithm

Highest Common Factor of 301,823,200 is 1

Step 1: Since 823 > 301, we apply the division lemma to 823 and 301, to get

823 = 301 x 2 + 221

Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 221 and 301, to get

301 = 221 x 1 + 80

Step 3: We consider the new divisor 221 and the new remainder 80, and apply the division lemma to get

221 = 80 x 2 + 61

We consider the new divisor 80 and the new remainder 61,and apply the division lemma to get

80 = 61 x 1 + 19

We consider the new divisor 61 and the new remainder 19,and apply the division lemma to get

61 = 19 x 3 + 4

We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get

19 = 4 x 4 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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 301 and 823 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(61,19) = HCF(80,61) = HCF(221,80) = HCF(301,221) = HCF(823,301) .

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

Step 1: Since 200 > 1, we apply the division lemma to 200 and 1, to get

200 = 1 x 200 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 200 is 1

Notice that 1 = HCF(200,1) .

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Frequently Asked Questions on HCF of 301, 823, 200 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 301, 823, 200?

Answer: HCF of 301, 823, 200 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 301, 823, 200 using Euclid's Algorithm?

Answer: For arbitrary numbers 301, 823, 200 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.