Highest Common Factor of 3778, 2200, 18057 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 3778, 2200, 18057 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3778, 2200, 18057 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 3778, 2200, 18057 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 3778, 2200, 18057 is 1.

HCF(3778, 2200, 18057) = 1

HCF of 3778, 2200, 18057 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 3778, 2200, 18057 is 1.

Highest Common Factor of 3778,2200,18057 using Euclid's algorithm

Highest Common Factor of 3778,2200,18057 is 1

Step 1: Since 3778 > 2200, we apply the division lemma to 3778 and 2200, to get

3778 = 2200 x 1 + 1578

Step 2: Since the reminder 2200 ≠ 0, we apply division lemma to 1578 and 2200, to get

2200 = 1578 x 1 + 622

Step 3: We consider the new divisor 1578 and the new remainder 622, and apply the division lemma to get

1578 = 622 x 2 + 334

We consider the new divisor 622 and the new remainder 334,and apply the division lemma to get

622 = 334 x 1 + 288

We consider the new divisor 334 and the new remainder 288,and apply the division lemma to get

334 = 288 x 1 + 46

We consider the new divisor 288 and the new remainder 46,and apply the division lemma to get

288 = 46 x 6 + 12

We consider the new divisor 46 and the new remainder 12,and apply the division lemma to get

46 = 12 x 3 + 10

We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get

12 = 10 x 1 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3778 and 2200 is 2

Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(46,12) = HCF(288,46) = HCF(334,288) = HCF(622,334) = HCF(1578,622) = HCF(2200,1578) = HCF(3778,2200) .

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

Step 1: Since 18057 > 2, we apply the division lemma to 18057 and 2, to get

18057 = 2 x 9028 + 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 18057 is 1

Notice that 1 = HCF(2,1) = HCF(18057,2) .

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Frequently Asked Questions on HCF of 3778, 2200, 18057 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 3778, 2200, 18057?

Answer: HCF of 3778, 2200, 18057 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3778, 2200, 18057 using Euclid's Algorithm?

Answer: For arbitrary numbers 3778, 2200, 18057 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.