Highest Common Factor of 2305, 9046, 37138 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 2305, 9046, 37138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2305, 9046, 37138 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 2305, 9046, 37138 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 2305, 9046, 37138 is 1.

HCF(2305, 9046, 37138) = 1

HCF of 2305, 9046, 37138 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 2305, 9046, 37138 is 1.

Highest Common Factor of 2305,9046,37138 using Euclid's algorithm

Highest Common Factor of 2305,9046,37138 is 1

Step 1: Since 9046 > 2305, we apply the division lemma to 9046 and 2305, to get

9046 = 2305 x 3 + 2131

Step 2: Since the reminder 2305 ≠ 0, we apply division lemma to 2131 and 2305, to get

2305 = 2131 x 1 + 174

Step 3: We consider the new divisor 2131 and the new remainder 174, and apply the division lemma to get

2131 = 174 x 12 + 43

We consider the new divisor 174 and the new remainder 43,and apply the division lemma to get

174 = 43 x 4 + 2

We consider the new divisor 43 and the new remainder 2,and apply the division lemma to get

43 = 2 x 21 + 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 2305 and 9046 is 1

Notice that 1 = HCF(2,1) = HCF(43,2) = HCF(174,43) = HCF(2131,174) = HCF(2305,2131) = HCF(9046,2305) .

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

Step 1: Since 37138 > 1, we apply the division lemma to 37138 and 1, to get

37138 = 1 x 37138 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 37138 is 1

Notice that 1 = HCF(37138,1) .

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Frequently Asked Questions on HCF of 2305, 9046, 37138 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 2305, 9046, 37138?

Answer: HCF of 2305, 9046, 37138 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2305, 9046, 37138 using Euclid's Algorithm?

Answer: For arbitrary numbers 2305, 9046, 37138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.