Highest Common Factor of 6074, 9869, 33912 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 6074, 9869, 33912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6074, 9869, 33912 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 6074, 9869, 33912 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 6074, 9869, 33912 is 1.

HCF(6074, 9869, 33912) = 1

HCF of 6074, 9869, 33912 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 6074, 9869, 33912 is 1.

Highest Common Factor of 6074,9869,33912 using Euclid's algorithm

Highest Common Factor of 6074,9869,33912 is 1

Step 1: Since 9869 > 6074, we apply the division lemma to 9869 and 6074, to get

9869 = 6074 x 1 + 3795

Step 2: Since the reminder 6074 ≠ 0, we apply division lemma to 3795 and 6074, to get

6074 = 3795 x 1 + 2279

Step 3: We consider the new divisor 3795 and the new remainder 2279, and apply the division lemma to get

3795 = 2279 x 1 + 1516

We consider the new divisor 2279 and the new remainder 1516,and apply the division lemma to get

2279 = 1516 x 1 + 763

We consider the new divisor 1516 and the new remainder 763,and apply the division lemma to get

1516 = 763 x 1 + 753

We consider the new divisor 763 and the new remainder 753,and apply the division lemma to get

763 = 753 x 1 + 10

We consider the new divisor 753 and the new remainder 10,and apply the division lemma to get

753 = 10 x 75 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 6074 and 9869 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(753,10) = HCF(763,753) = HCF(1516,763) = HCF(2279,1516) = HCF(3795,2279) = HCF(6074,3795) = HCF(9869,6074) .

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

Step 1: Since 33912 > 1, we apply the division lemma to 33912 and 1, to get

33912 = 1 x 33912 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 33912 is 1

Notice that 1 = HCF(33912,1) .

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Frequently Asked Questions on HCF of 6074, 9869, 33912 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 6074, 9869, 33912?

Answer: HCF of 6074, 9869, 33912 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6074, 9869, 33912 using Euclid's Algorithm?

Answer: For arbitrary numbers 6074, 9869, 33912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.