Highest Common Factor of 2105, 8969, 29275 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 2105, 8969, 29275 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2105, 8969, 29275 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 2105, 8969, 29275 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 2105, 8969, 29275 is 1.

HCF(2105, 8969, 29275) = 1

HCF of 2105, 8969, 29275 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 2105, 8969, 29275 is 1.

Highest Common Factor of 2105,8969,29275 using Euclid's algorithm

Highest Common Factor of 2105,8969,29275 is 1

Step 1: Since 8969 > 2105, we apply the division lemma to 8969 and 2105, to get

8969 = 2105 x 4 + 549

Step 2: Since the reminder 2105 ≠ 0, we apply division lemma to 549 and 2105, to get

2105 = 549 x 3 + 458

Step 3: We consider the new divisor 549 and the new remainder 458, and apply the division lemma to get

549 = 458 x 1 + 91

We consider the new divisor 458 and the new remainder 91,and apply the division lemma to get

458 = 91 x 5 + 3

We consider the new divisor 91 and the new remainder 3,and apply the division lemma to get

91 = 3 x 30 + 1

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 2105 and 8969 is 1

Notice that 1 = HCF(3,1) = HCF(91,3) = HCF(458,91) = HCF(549,458) = HCF(2105,549) = HCF(8969,2105) .

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

Step 1: Since 29275 > 1, we apply the division lemma to 29275 and 1, to get

29275 = 1 x 29275 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 29275 is 1

Notice that 1 = HCF(29275,1) .

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Frequently Asked Questions on HCF of 2105, 8969, 29275 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 2105, 8969, 29275?

Answer: HCF of 2105, 8969, 29275 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2105, 8969, 29275 using Euclid's Algorithm?

Answer: For arbitrary numbers 2105, 8969, 29275 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.