Highest Common Factor of 8408, 2353 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 8408, 2353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8408, 2353 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 8408, 2353 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 8408, 2353 is 1.

HCF(8408, 2353) = 1

HCF of 8408, 2353 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 8408, 2353 is 1.

Highest Common Factor of 8408,2353 using Euclid's algorithm

Highest Common Factor of 8408,2353 is 1

Step 1: Since 8408 > 2353, we apply the division lemma to 8408 and 2353, to get

8408 = 2353 x 3 + 1349

Step 2: Since the reminder 2353 ≠ 0, we apply division lemma to 1349 and 2353, to get

2353 = 1349 x 1 + 1004

Step 3: We consider the new divisor 1349 and the new remainder 1004, and apply the division lemma to get

1349 = 1004 x 1 + 345

We consider the new divisor 1004 and the new remainder 345,and apply the division lemma to get

1004 = 345 x 2 + 314

We consider the new divisor 345 and the new remainder 314,and apply the division lemma to get

345 = 314 x 1 + 31

We consider the new divisor 314 and the new remainder 31,and apply the division lemma to get

314 = 31 x 10 + 4

We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get

31 = 4 x 7 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8408 and 2353 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(314,31) = HCF(345,314) = HCF(1004,345) = HCF(1349,1004) = HCF(2353,1349) = HCF(8408,2353) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 8408, 2353 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 8408, 2353?

Answer: HCF of 8408, 2353 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8408, 2353 using Euclid's Algorithm?

Answer: For arbitrary numbers 8408, 2353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.