Highest Common Factor of 1837, 3400 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 1837, 3400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1837, 3400 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 1837, 3400 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 1837, 3400 is 1.

HCF(1837, 3400) = 1

HCF of 1837, 3400 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 1837, 3400 is 1.

Highest Common Factor of 1837,3400 using Euclid's algorithm

Highest Common Factor of 1837,3400 is 1

Step 1: Since 3400 > 1837, we apply the division lemma to 3400 and 1837, to get

3400 = 1837 x 1 + 1563

Step 2: Since the reminder 1837 ≠ 0, we apply division lemma to 1563 and 1837, to get

1837 = 1563 x 1 + 274

Step 3: We consider the new divisor 1563 and the new remainder 274, and apply the division lemma to get

1563 = 274 x 5 + 193

We consider the new divisor 274 and the new remainder 193,and apply the division lemma to get

274 = 193 x 1 + 81

We consider the new divisor 193 and the new remainder 81,and apply the division lemma to get

193 = 81 x 2 + 31

We consider the new divisor 81 and the new remainder 31,and apply the division lemma to get

81 = 31 x 2 + 19

We consider the new divisor 31 and the new remainder 19,and apply the division lemma to get

31 = 19 x 1 + 12

We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get

19 = 12 x 1 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 1837 and 3400 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(31,19) = HCF(81,31) = HCF(193,81) = HCF(274,193) = HCF(1563,274) = HCF(1837,1563) = HCF(3400,1837) .

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Frequently Asked Questions on HCF of 1837, 3400 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 1837, 3400?

Answer: HCF of 1837, 3400 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1837, 3400 using Euclid's Algorithm?

Answer: For arbitrary numbers 1837, 3400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.