Highest Common Factor of 2313, 6505, 32351 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 2313, 6505, 32351 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2313, 6505, 32351 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 2313, 6505, 32351 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 2313, 6505, 32351 is 1.

HCF(2313, 6505, 32351) = 1

HCF of 2313, 6505, 32351 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 2313, 6505, 32351 is 1.

Highest Common Factor of 2313,6505,32351 using Euclid's algorithm

Highest Common Factor of 2313,6505,32351 is 1

Step 1: Since 6505 > 2313, we apply the division lemma to 6505 and 2313, to get

6505 = 2313 x 2 + 1879

Step 2: Since the reminder 2313 ≠ 0, we apply division lemma to 1879 and 2313, to get

2313 = 1879 x 1 + 434

Step 3: We consider the new divisor 1879 and the new remainder 434, and apply the division lemma to get

1879 = 434 x 4 + 143

We consider the new divisor 434 and the new remainder 143,and apply the division lemma to get

434 = 143 x 3 + 5

We consider the new divisor 143 and the new remainder 5,and apply the division lemma to get

143 = 5 x 28 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 2313 and 6505 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(143,5) = HCF(434,143) = HCF(1879,434) = HCF(2313,1879) = HCF(6505,2313) .

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

Step 1: Since 32351 > 1, we apply the division lemma to 32351 and 1, to get

32351 = 1 x 32351 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32351 is 1

Notice that 1 = HCF(32351,1) .

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Frequently Asked Questions on HCF of 2313, 6505, 32351 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 2313, 6505, 32351?

Answer: HCF of 2313, 6505, 32351 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2313, 6505, 32351 using Euclid's Algorithm?

Answer: For arbitrary numbers 2313, 6505, 32351 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.