Highest Common Factor of 9825, 6746 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 9825, 6746 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9825, 6746 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 9825, 6746 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 9825, 6746 is 1.

HCF(9825, 6746) = 1

HCF of 9825, 6746 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 9825, 6746 is 1.

Highest Common Factor of 9825,6746 using Euclid's algorithm

Highest Common Factor of 9825,6746 is 1

Step 1: Since 9825 > 6746, we apply the division lemma to 9825 and 6746, to get

9825 = 6746 x 1 + 3079

Step 2: Since the reminder 6746 ≠ 0, we apply division lemma to 3079 and 6746, to get

6746 = 3079 x 2 + 588

Step 3: We consider the new divisor 3079 and the new remainder 588, and apply the division lemma to get

3079 = 588 x 5 + 139

We consider the new divisor 588 and the new remainder 139,and apply the division lemma to get

588 = 139 x 4 + 32

We consider the new divisor 139 and the new remainder 32,and apply the division lemma to get

139 = 32 x 4 + 11

We consider the new divisor 32 and the new remainder 11,and apply the division lemma to get

32 = 11 x 2 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9825 and 6746 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(32,11) = HCF(139,32) = HCF(588,139) = HCF(3079,588) = HCF(6746,3079) = HCF(9825,6746) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 9825, 6746 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 9825, 6746?

Answer: HCF of 9825, 6746 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9825, 6746 using Euclid's Algorithm?

Answer: For arbitrary numbers 9825, 6746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.