Highest Common Factor of 5844, 3542, 75874 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 5844, 3542, 75874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 5844, 3542, 75874 is 2 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 5844, 3542, 75874 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 5844, 3542, 75874 is 2.

HCF(5844, 3542, 75874) = 2

HCF of 5844, 3542, 75874 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 5844, 3542, 75874 is 2.

Highest Common Factor of 5844,3542,75874 using Euclid's algorithm

Highest Common Factor of 5844,3542,75874 is 2

Step 1: Since 5844 > 3542, we apply the division lemma to 5844 and 3542, to get

5844 = 3542 x 1 + 2302

Step 2: Since the reminder 3542 ≠ 0, we apply division lemma to 2302 and 3542, to get

3542 = 2302 x 1 + 1240

Step 3: We consider the new divisor 2302 and the new remainder 1240, and apply the division lemma to get

2302 = 1240 x 1 + 1062

We consider the new divisor 1240 and the new remainder 1062,and apply the division lemma to get

1240 = 1062 x 1 + 178

We consider the new divisor 1062 and the new remainder 178,and apply the division lemma to get

1062 = 178 x 5 + 172

We consider the new divisor 178 and the new remainder 172,and apply the division lemma to get

178 = 172 x 1 + 6

We consider the new divisor 172 and the new remainder 6,and apply the division lemma to get

172 = 6 x 28 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 5844 and 3542 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(172,6) = HCF(178,172) = HCF(1062,178) = HCF(1240,1062) = HCF(2302,1240) = HCF(3542,2302) = HCF(5844,3542) .

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

Step 1: Since 75874 > 2, we apply the division lemma to 75874 and 2, to get

75874 = 2 x 37937 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 75874 is 2

Notice that 2 = HCF(75874,2) .

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Frequently Asked Questions on HCF of 5844, 3542, 75874 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 5844, 3542, 75874?

Answer: HCF of 5844, 3542, 75874 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5844, 3542, 75874 using Euclid's Algorithm?

Answer: For arbitrary numbers 5844, 3542, 75874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.