Highest Common Factor of 2301, 8306 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 2301, 8306 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2301, 8306 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 2301, 8306 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 2301, 8306 is 1.

HCF(2301, 8306) = 1

HCF of 2301, 8306 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 2301, 8306 is 1.

Highest Common Factor of 2301,8306 using Euclid's algorithm

Highest Common Factor of 2301,8306 is 1

Step 1: Since 8306 > 2301, we apply the division lemma to 8306 and 2301, to get

8306 = 2301 x 3 + 1403

Step 2: Since the reminder 2301 ≠ 0, we apply division lemma to 1403 and 2301, to get

2301 = 1403 x 1 + 898

Step 3: We consider the new divisor 1403 and the new remainder 898, and apply the division lemma to get

1403 = 898 x 1 + 505

We consider the new divisor 898 and the new remainder 505,and apply the division lemma to get

898 = 505 x 1 + 393

We consider the new divisor 505 and the new remainder 393,and apply the division lemma to get

505 = 393 x 1 + 112

We consider the new divisor 393 and the new remainder 112,and apply the division lemma to get

393 = 112 x 3 + 57

We consider the new divisor 112 and the new remainder 57,and apply the division lemma to get

112 = 57 x 1 + 55

We consider the new divisor 57 and the new remainder 55,and apply the division lemma to get

57 = 55 x 1 + 2

We consider the new divisor 55 and the new remainder 2,and apply the division lemma to get

55 = 2 x 27 + 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 2301 and 8306 is 1

Notice that 1 = HCF(2,1) = HCF(55,2) = HCF(57,55) = HCF(112,57) = HCF(393,112) = HCF(505,393) = HCF(898,505) = HCF(1403,898) = HCF(2301,1403) = HCF(8306,2301) .

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Frequently Asked Questions on HCF of 2301, 8306 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 2301, 8306?

Answer: HCF of 2301, 8306 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2301, 8306 using Euclid's Algorithm?

Answer: For arbitrary numbers 2301, 8306 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.