Highest Common Factor of 980, 204, 203 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 980, 204, 203 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 980, 204, 203 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 980, 204, 203 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 980, 204, 203 is 1.

HCF(980, 204, 203) = 1

HCF of 980, 204, 203 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 980, 204, 203 is 1.

Highest Common Factor of 980,204,203 using Euclid's algorithm

Highest Common Factor of 980,204,203 is 1

Step 1: Since 980 > 204, we apply the division lemma to 980 and 204, to get

980 = 204 x 4 + 164

Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 164 and 204, to get

204 = 164 x 1 + 40

Step 3: We consider the new divisor 164 and the new remainder 40, and apply the division lemma to get

164 = 40 x 4 + 4

We consider the new divisor 40 and the new remainder 4, and apply the division lemma to get

40 = 4 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 980 and 204 is 4

Notice that 4 = HCF(40,4) = HCF(164,40) = HCF(204,164) = HCF(980,204) .

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

Step 1: Since 203 > 4, we apply the division lemma to 203 and 4, to get

203 = 4 x 50 + 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 203 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(203,4) .

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Frequently Asked Questions on HCF of 980, 204, 203 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 980, 204, 203?

Answer: HCF of 980, 204, 203 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 980, 204, 203 using Euclid's Algorithm?

Answer: For arbitrary numbers 980, 204, 203 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.