Highest Common Factor of 8356, 6448, 16426 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 8356, 6448, 16426 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 8356, 6448, 16426 is 2 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 8356, 6448, 16426 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 8356, 6448, 16426 is 2.

HCF(8356, 6448, 16426) = 2

HCF of 8356, 6448, 16426 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 8356, 6448, 16426 is 2.

Highest Common Factor of 8356,6448,16426 using Euclid's algorithm

Highest Common Factor of 8356,6448,16426 is 2

Step 1: Since 8356 > 6448, we apply the division lemma to 8356 and 6448, to get

8356 = 6448 x 1 + 1908

Step 2: Since the reminder 6448 ≠ 0, we apply division lemma to 1908 and 6448, to get

6448 = 1908 x 3 + 724

Step 3: We consider the new divisor 1908 and the new remainder 724, and apply the division lemma to get

1908 = 724 x 2 + 460

We consider the new divisor 724 and the new remainder 460,and apply the division lemma to get

724 = 460 x 1 + 264

We consider the new divisor 460 and the new remainder 264,and apply the division lemma to get

460 = 264 x 1 + 196

We consider the new divisor 264 and the new remainder 196,and apply the division lemma to get

264 = 196 x 1 + 68

We consider the new divisor 196 and the new remainder 68,and apply the division lemma to get

196 = 68 x 2 + 60

We consider the new divisor 68 and the new remainder 60,and apply the division lemma to get

68 = 60 x 1 + 8

We consider the new divisor 60 and the new remainder 8,and apply the division lemma to get

60 = 8 x 7 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8356 and 6448 is 4

Notice that 4 = HCF(8,4) = HCF(60,8) = HCF(68,60) = HCF(196,68) = HCF(264,196) = HCF(460,264) = HCF(724,460) = HCF(1908,724) = HCF(6448,1908) = HCF(8356,6448) .

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

Step 1: Since 16426 > 4, we apply the division lemma to 16426 and 4, to get

16426 = 4 x 4106 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 16426 is 2

Notice that 2 = HCF(4,2) = HCF(16426,4) .

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Frequently Asked Questions on HCF of 8356, 6448, 16426 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 8356, 6448, 16426?

Answer: HCF of 8356, 6448, 16426 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8356, 6448, 16426 using Euclid's Algorithm?

Answer: For arbitrary numbers 8356, 6448, 16426 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.