Highest Common Factor of 585, 988, 262 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 585, 988, 262 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 988, 262 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 585, 988, 262 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 585, 988, 262 is 1.

HCF(585, 988, 262) = 1

HCF of 585, 988, 262 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 585, 988, 262 is 1.

Highest Common Factor of 585,988,262 using Euclid's algorithm

Highest Common Factor of 585,988,262 is 1

Step 1: Since 988 > 585, we apply the division lemma to 988 and 585, to get

988 = 585 x 1 + 403

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 403 and 585, to get

585 = 403 x 1 + 182

Step 3: We consider the new divisor 403 and the new remainder 182, and apply the division lemma to get

403 = 182 x 2 + 39

We consider the new divisor 182 and the new remainder 39,and apply the division lemma to get

182 = 39 x 4 + 26

We consider the new divisor 39 and the new remainder 26,and apply the division lemma to get

39 = 26 x 1 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 585 and 988 is 13

Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(182,39) = HCF(403,182) = HCF(585,403) = HCF(988,585) .

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

Step 1: Since 262 > 13, we apply the division lemma to 262 and 13, to get

262 = 13 x 20 + 2

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 2 and 13, to get

13 = 2 x 6 + 1

Step 3: 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 13 and 262 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(262,13) .

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Frequently Asked Questions on HCF of 585, 988, 262 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 585, 988, 262?

Answer: HCF of 585, 988, 262 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 988, 262 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 988, 262 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.