Highest Common Factor of 590, 746, 994 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 590, 746, 994 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 590, 746, 994 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 590, 746, 994 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 590, 746, 994 is 2.

HCF(590, 746, 994) = 2

HCF of 590, 746, 994 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 590, 746, 994 is 2.

Highest Common Factor of 590,746,994 using Euclid's algorithm

Highest Common Factor of 590,746,994 is 2

Step 1: Since 746 > 590, we apply the division lemma to 746 and 590, to get

746 = 590 x 1 + 156

Step 2: Since the reminder 590 ≠ 0, we apply division lemma to 156 and 590, to get

590 = 156 x 3 + 122

Step 3: We consider the new divisor 156 and the new remainder 122, and apply the division lemma to get

156 = 122 x 1 + 34

We consider the new divisor 122 and the new remainder 34,and apply the division lemma to get

122 = 34 x 3 + 20

We consider the new divisor 34 and the new remainder 20,and apply the division lemma to get

34 = 20 x 1 + 14

We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get

20 = 14 x 1 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 590 and 746 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(34,20) = HCF(122,34) = HCF(156,122) = HCF(590,156) = HCF(746,590) .

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

Step 1: Since 994 > 2, we apply the division lemma to 994 and 2, to get

994 = 2 x 497 + 0

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

Notice that 2 = HCF(994,2) .

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Frequently Asked Questions on HCF of 590, 746, 994 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 590, 746, 994?

Answer: HCF of 590, 746, 994 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 590, 746, 994 using Euclid's Algorithm?

Answer: For arbitrary numbers 590, 746, 994 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.