Highest Common Factor of 490, 206, 751 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 490, 206, 751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 490, 206, 751 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 490, 206, 751 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 490, 206, 751 is 1.

HCF(490, 206, 751) = 1

HCF of 490, 206, 751 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 490, 206, 751 is 1.

Highest Common Factor of 490,206,751 using Euclid's algorithm

Highest Common Factor of 490,206,751 is 1

Step 1: Since 490 > 206, we apply the division lemma to 490 and 206, to get

490 = 206 x 2 + 78

Step 2: Since the reminder 206 ≠ 0, we apply division lemma to 78 and 206, to get

206 = 78 x 2 + 50

Step 3: We consider the new divisor 78 and the new remainder 50, and apply the division lemma to get

78 = 50 x 1 + 28

We consider the new divisor 50 and the new remainder 28,and apply the division lemma to get

50 = 28 x 1 + 22

We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get

28 = 22 x 1 + 6

We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get

22 = 6 x 3 + 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 490 and 206 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(50,28) = HCF(78,50) = HCF(206,78) = HCF(490,206) .

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

Step 1: Since 751 > 2, we apply the division lemma to 751 and 2, to get

751 = 2 x 375 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 751 is 1

Notice that 1 = HCF(2,1) = HCF(751,2) .

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Frequently Asked Questions on HCF of 490, 206, 751 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 490, 206, 751?

Answer: HCF of 490, 206, 751 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 490, 206, 751 using Euclid's Algorithm?

Answer: For arbitrary numbers 490, 206, 751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.