Highest Common Factor of 206, 994, 620 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 206, 994, 620 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 206, 994, 620 is 2 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 206, 994, 620 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 206, 994, 620 is 2.

HCF(206, 994, 620) = 2

HCF of 206, 994, 620 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 206, 994, 620 is 2.

Highest Common Factor of 206,994,620 using Euclid's algorithm

Highest Common Factor of 206,994,620 is 2

Step 1: Since 994 > 206, we apply the division lemma to 994 and 206, to get

994 = 206 x 4 + 170

Step 2: Since the reminder 206 ≠ 0, we apply division lemma to 170 and 206, to get

206 = 170 x 1 + 36

Step 3: We consider the new divisor 170 and the new remainder 36, and apply the division lemma to get

170 = 36 x 4 + 26

We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get

36 = 26 x 1 + 10

We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get

26 = 10 x 2 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 206 and 994 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(170,36) = HCF(206,170) = HCF(994,206) .

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

Step 1: Since 620 > 2, we apply the division lemma to 620 and 2, to get

620 = 2 x 310 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 620 is 2

Notice that 2 = HCF(620,2) .

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Frequently Asked Questions on HCF of 206, 994, 620 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 206, 994, 620?

Answer: HCF of 206, 994, 620 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 206, 994, 620 using Euclid's Algorithm?

Answer: For arbitrary numbers 206, 994, 620 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.