Highest Common Factor of 1108, 8670, 23281 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 1108, 8670, 23281 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1108, 8670, 23281 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 1108, 8670, 23281 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 1108, 8670, 23281 is 1.

HCF(1108, 8670, 23281) = 1

HCF of 1108, 8670, 23281 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 1108, 8670, 23281 is 1.

Highest Common Factor of 1108,8670,23281 using Euclid's algorithm

Highest Common Factor of 1108,8670,23281 is 1

Step 1: Since 8670 > 1108, we apply the division lemma to 8670 and 1108, to get

8670 = 1108 x 7 + 914

Step 2: Since the reminder 1108 ≠ 0, we apply division lemma to 914 and 1108, to get

1108 = 914 x 1 + 194

Step 3: We consider the new divisor 914 and the new remainder 194, and apply the division lemma to get

914 = 194 x 4 + 138

We consider the new divisor 194 and the new remainder 138,and apply the division lemma to get

194 = 138 x 1 + 56

We consider the new divisor 138 and the new remainder 56,and apply the division lemma to get

138 = 56 x 2 + 26

We consider the new divisor 56 and the new remainder 26,and apply the division lemma to get

56 = 26 x 2 + 4

We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get

26 = 4 x 6 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1108 and 8670 is 2

Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(56,26) = HCF(138,56) = HCF(194,138) = HCF(914,194) = HCF(1108,914) = HCF(8670,1108) .

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

Step 1: Since 23281 > 2, we apply the division lemma to 23281 and 2, to get

23281 = 2 x 11640 + 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 23281 is 1

Notice that 1 = HCF(2,1) = HCF(23281,2) .

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Frequently Asked Questions on HCF of 1108, 8670, 23281 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 1108, 8670, 23281?

Answer: HCF of 1108, 8670, 23281 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1108, 8670, 23281 using Euclid's Algorithm?

Answer: For arbitrary numbers 1108, 8670, 23281 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.