Highest Common Factor of 3521, 6504 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 3521, 6504 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3521, 6504 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 3521, 6504 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 3521, 6504 is 1.

HCF(3521, 6504) = 1

HCF of 3521, 6504 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 3521, 6504 is 1.

Highest Common Factor of 3521,6504 using Euclid's algorithm

Highest Common Factor of 3521,6504 is 1

Step 1: Since 6504 > 3521, we apply the division lemma to 6504 and 3521, to get

6504 = 3521 x 1 + 2983

Step 2: Since the reminder 3521 ≠ 0, we apply division lemma to 2983 and 3521, to get

3521 = 2983 x 1 + 538

Step 3: We consider the new divisor 2983 and the new remainder 538, and apply the division lemma to get

2983 = 538 x 5 + 293

We consider the new divisor 538 and the new remainder 293,and apply the division lemma to get

538 = 293 x 1 + 245

We consider the new divisor 293 and the new remainder 245,and apply the division lemma to get

293 = 245 x 1 + 48

We consider the new divisor 245 and the new remainder 48,and apply the division lemma to get

245 = 48 x 5 + 5

We consider the new divisor 48 and the new remainder 5,and apply the division lemma to get

48 = 5 x 9 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3521 and 6504 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(48,5) = HCF(245,48) = HCF(293,245) = HCF(538,293) = HCF(2983,538) = HCF(3521,2983) = HCF(6504,3521) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 3521, 6504 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 3521, 6504?

Answer: HCF of 3521, 6504 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3521, 6504 using Euclid's Algorithm?

Answer: For arbitrary numbers 3521, 6504 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.