Highest Common Factor of 6000, 9526, 27118 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 6000, 9526, 27118 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6000, 9526, 27118 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 6000, 9526, 27118 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 6000, 9526, 27118 is 2.

HCF(6000, 9526, 27118) = 2

HCF of 6000, 9526, 27118 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 6000, 9526, 27118 is 2.

Highest Common Factor of 6000,9526,27118 using Euclid's algorithm

Highest Common Factor of 6000,9526,27118 is 2

Step 1: Since 9526 > 6000, we apply the division lemma to 9526 and 6000, to get

9526 = 6000 x 1 + 3526

Step 2: Since the reminder 6000 ≠ 0, we apply division lemma to 3526 and 6000, to get

6000 = 3526 x 1 + 2474

Step 3: We consider the new divisor 3526 and the new remainder 2474, and apply the division lemma to get

3526 = 2474 x 1 + 1052

We consider the new divisor 2474 and the new remainder 1052,and apply the division lemma to get

2474 = 1052 x 2 + 370

We consider the new divisor 1052 and the new remainder 370,and apply the division lemma to get

1052 = 370 x 2 + 312

We consider the new divisor 370 and the new remainder 312,and apply the division lemma to get

370 = 312 x 1 + 58

We consider the new divisor 312 and the new remainder 58,and apply the division lemma to get

312 = 58 x 5 + 22

We consider the new divisor 58 and the new remainder 22,and apply the division lemma to get

58 = 22 x 2 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6000 and 9526 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(58,22) = HCF(312,58) = HCF(370,312) = HCF(1052,370) = HCF(2474,1052) = HCF(3526,2474) = HCF(6000,3526) = HCF(9526,6000) .


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

Step 1: Since 27118 > 2, we apply the division lemma to 27118 and 2, to get

27118 = 2 x 13559 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 27118 is 2

Notice that 2 = HCF(27118,2) .

HCF using Euclid's Algorithm Calculation Examples

Frequently Asked Questions on HCF of 6000, 9526, 27118 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 6000, 9526, 27118?

Answer: HCF of 6000, 9526, 27118 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6000, 9526, 27118 using Euclid's Algorithm?

Answer: For arbitrary numbers 6000, 9526, 27118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.