Highest Common Factor of 8588, 2488, 13691 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 8588, 2488, 13691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8588, 2488, 13691 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 8588, 2488, 13691 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 8588, 2488, 13691 is 1.

HCF(8588, 2488, 13691) = 1

HCF of 8588, 2488, 13691 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 8588, 2488, 13691 is 1.

Highest Common Factor of 8588,2488,13691 using Euclid's algorithm

Highest Common Factor of 8588,2488,13691 is 1

Step 1: Since 8588 > 2488, we apply the division lemma to 8588 and 2488, to get

8588 = 2488 x 3 + 1124

Step 2: Since the reminder 2488 ≠ 0, we apply division lemma to 1124 and 2488, to get

2488 = 1124 x 2 + 240

Step 3: We consider the new divisor 1124 and the new remainder 240, and apply the division lemma to get

1124 = 240 x 4 + 164

We consider the new divisor 240 and the new remainder 164,and apply the division lemma to get

240 = 164 x 1 + 76

We consider the new divisor 164 and the new remainder 76,and apply the division lemma to get

164 = 76 x 2 + 12

We consider the new divisor 76 and the new remainder 12,and apply the division lemma to get

76 = 12 x 6 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8588 and 2488 is 4

Notice that 4 = HCF(12,4) = HCF(76,12) = HCF(164,76) = HCF(240,164) = HCF(1124,240) = HCF(2488,1124) = HCF(8588,2488) .

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

Step 1: Since 13691 > 4, we apply the division lemma to 13691 and 4, to get

13691 = 4 x 3422 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 4 and 13691 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(13691,4) .

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Frequently Asked Questions on HCF of 8588, 2488, 13691 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 8588, 2488, 13691?

Answer: HCF of 8588, 2488, 13691 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8588, 2488, 13691 using Euclid's Algorithm?

Answer: For arbitrary numbers 8588, 2488, 13691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.