Highest Common Factor of 363, 588, 490 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 363, 588, 490 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 363, 588, 490 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 363, 588, 490 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 363, 588, 490 is 1.

HCF(363, 588, 490) = 1

HCF of 363, 588, 490 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 363, 588, 490 is 1.

Highest Common Factor of 363,588,490 using Euclid's algorithm

Highest Common Factor of 363,588,490 is 1

Step 1: Since 588 > 363, we apply the division lemma to 588 and 363, to get

588 = 363 x 1 + 225

Step 2: Since the reminder 363 ≠ 0, we apply division lemma to 225 and 363, to get

363 = 225 x 1 + 138

Step 3: We consider the new divisor 225 and the new remainder 138, and apply the division lemma to get

225 = 138 x 1 + 87

We consider the new divisor 138 and the new remainder 87,and apply the division lemma to get

138 = 87 x 1 + 51

We consider the new divisor 87 and the new remainder 51,and apply the division lemma to get

87 = 51 x 1 + 36

We consider the new divisor 51 and the new remainder 36,and apply the division lemma to get

51 = 36 x 1 + 15

We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get

36 = 15 x 2 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 363 and 588 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(51,36) = HCF(87,51) = HCF(138,87) = HCF(225,138) = HCF(363,225) = HCF(588,363) .

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

Step 1: Since 490 > 3, we apply the division lemma to 490 and 3, to get

490 = 3 x 163 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 490 is 1

Notice that 1 = HCF(3,1) = HCF(490,3) .

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Frequently Asked Questions on HCF of 363, 588, 490 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 363, 588, 490?

Answer: HCF of 363, 588, 490 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 363, 588, 490 using Euclid's Algorithm?

Answer: For arbitrary numbers 363, 588, 490 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.