Highest Common Factor of 8749, 6409 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 8749, 6409 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 8749, 6409 is 13 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 8749, 6409 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 8749, 6409 is 13.

HCF(8749, 6409) = 13

HCF of 8749, 6409 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 8749, 6409 is 13.

Highest Common Factor of 8749,6409 using Euclid's algorithm

Highest Common Factor of 8749,6409 is 13

Step 1: Since 8749 > 6409, we apply the division lemma to 8749 and 6409, to get

8749 = 6409 x 1 + 2340

Step 2: Since the reminder 6409 ≠ 0, we apply division lemma to 2340 and 6409, to get

6409 = 2340 x 2 + 1729

Step 3: We consider the new divisor 2340 and the new remainder 1729, and apply the division lemma to get

2340 = 1729 x 1 + 611

We consider the new divisor 1729 and the new remainder 611,and apply the division lemma to get

1729 = 611 x 2 + 507

We consider the new divisor 611 and the new remainder 507,and apply the division lemma to get

611 = 507 x 1 + 104

We consider the new divisor 507 and the new remainder 104,and apply the division lemma to get

507 = 104 x 4 + 91

We consider the new divisor 104 and the new remainder 91,and apply the division lemma to get

104 = 91 x 1 + 13

We consider the new divisor 91 and the new remainder 13,and apply the division lemma to get

91 = 13 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 8749 and 6409 is 13

Notice that 13 = HCF(91,13) = HCF(104,91) = HCF(507,104) = HCF(611,507) = HCF(1729,611) = HCF(2340,1729) = HCF(6409,2340) = HCF(8749,6409) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 8749, 6409 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 8749, 6409?

Answer: HCF of 8749, 6409 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8749, 6409 using Euclid's Algorithm?

Answer: For arbitrary numbers 8749, 6409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.