Highest Common Factor of 305, 584, 998, 592 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 305, 584, 998, 592 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 305, 584, 998, 592 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 305, 584, 998, 592 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 305, 584, 998, 592 is 1.

HCF(305, 584, 998, 592) = 1

HCF of 305, 584, 998, 592 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 305, 584, 998, 592 is 1.

Highest Common Factor of 305,584,998,592 using Euclid's algorithm

Highest Common Factor of 305,584,998,592 is 1

Step 1: Since 584 > 305, we apply the division lemma to 584 and 305, to get

584 = 305 x 1 + 279

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 279 and 305, to get

305 = 279 x 1 + 26

Step 3: We consider the new divisor 279 and the new remainder 26, and apply the division lemma to get

279 = 26 x 10 + 19

We consider the new divisor 26 and the new remainder 19,and apply the division lemma to get

26 = 19 x 1 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 305 and 584 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(26,19) = HCF(279,26) = HCF(305,279) = HCF(584,305) .

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

Step 1: Since 998 > 1, we apply the division lemma to 998 and 1, to get

998 = 1 x 998 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 998 is 1

Notice that 1 = HCF(998,1) .

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

Step 1: Since 592 > 1, we apply the division lemma to 592 and 1, to get

592 = 1 x 592 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 592 is 1

Notice that 1 = HCF(592,1) .

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Frequently Asked Questions on HCF of 305, 584, 998, 592 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 305, 584, 998, 592?

Answer: HCF of 305, 584, 998, 592 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 305, 584, 998, 592 using Euclid's Algorithm?

Answer: For arbitrary numbers 305, 584, 998, 592 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.