Highest Common Factor of 724, 990, 396, 491 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 724, 990, 396, 491 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 724, 990, 396, 491 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 724, 990, 396, 491 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 724, 990, 396, 491 is 1.

HCF(724, 990, 396, 491) = 1

HCF of 724, 990, 396, 491 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 724, 990, 396, 491 is 1.

Highest Common Factor of 724,990,396,491 using Euclid's algorithm

Highest Common Factor of 724,990,396,491 is 1

Step 1: Since 990 > 724, we apply the division lemma to 990 and 724, to get

990 = 724 x 1 + 266

Step 2: Since the reminder 724 ≠ 0, we apply division lemma to 266 and 724, to get

724 = 266 x 2 + 192

Step 3: We consider the new divisor 266 and the new remainder 192, and apply the division lemma to get

266 = 192 x 1 + 74

We consider the new divisor 192 and the new remainder 74,and apply the division lemma to get

192 = 74 x 2 + 44

We consider the new divisor 74 and the new remainder 44,and apply the division lemma to get

74 = 44 x 1 + 30

We consider the new divisor 44 and the new remainder 30,and apply the division lemma to get

44 = 30 x 1 + 14

We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get

30 = 14 x 2 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 724 and 990 is 2

Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(44,30) = HCF(74,44) = HCF(192,74) = HCF(266,192) = HCF(724,266) = HCF(990,724) .

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

Step 1: Since 396 > 2, we apply the division lemma to 396 and 2, to get

396 = 2 x 198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 396 is 2

Notice that 2 = HCF(396,2) .

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

Step 1: Since 491 > 2, we apply the division lemma to 491 and 2, to get

491 = 2 x 245 + 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 491 is 1

Notice that 1 = HCF(2,1) = HCF(491,2) .

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Frequently Asked Questions on HCF of 724, 990, 396, 491 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 724, 990, 396, 491?

Answer: HCF of 724, 990, 396, 491 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 724, 990, 396, 491 using Euclid's Algorithm?

Answer: For arbitrary numbers 724, 990, 396, 491 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.