Highest Common Factor of 528, 6659 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 528, 6659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 528, 6659 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 528, 6659 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 528, 6659 is 1.

HCF(528, 6659) = 1

HCF of 528, 6659 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 528, 6659 is 1.

Highest Common Factor of 528,6659 using Euclid's algorithm

Highest Common Factor of 528,6659 is 1

Step 1: Since 6659 > 528, we apply the division lemma to 6659 and 528, to get

6659 = 528 x 12 + 323

Step 2: Since the reminder 528 ≠ 0, we apply division lemma to 323 and 528, to get

528 = 323 x 1 + 205

Step 3: We consider the new divisor 323 and the new remainder 205, and apply the division lemma to get

323 = 205 x 1 + 118

We consider the new divisor 205 and the new remainder 118,and apply the division lemma to get

205 = 118 x 1 + 87

We consider the new divisor 118 and the new remainder 87,and apply the division lemma to get

118 = 87 x 1 + 31

We consider the new divisor 87 and the new remainder 31,and apply the division lemma to get

87 = 31 x 2 + 25

We consider the new divisor 31 and the new remainder 25,and apply the division lemma to get

31 = 25 x 1 + 6

We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get

25 = 6 x 4 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 528 and 6659 is 1

Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(31,25) = HCF(87,31) = HCF(118,87) = HCF(205,118) = HCF(323,205) = HCF(528,323) = HCF(6659,528) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 528, 6659 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 528, 6659?

Answer: HCF of 528, 6659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 528, 6659 using Euclid's Algorithm?

Answer: For arbitrary numbers 528, 6659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.