Highest Common Factor of 8544, 1535 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 8544, 1535 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8544, 1535 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 8544, 1535 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 8544, 1535 is 1.

HCF(8544, 1535) = 1

HCF of 8544, 1535 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 8544, 1535 is 1.

Highest Common Factor of 8544,1535 using Euclid's algorithm

Highest Common Factor of 8544,1535 is 1

Step 1: Since 8544 > 1535, we apply the division lemma to 8544 and 1535, to get

8544 = 1535 x 5 + 869

Step 2: Since the reminder 1535 ≠ 0, we apply division lemma to 869 and 1535, to get

1535 = 869 x 1 + 666

Step 3: We consider the new divisor 869 and the new remainder 666, and apply the division lemma to get

869 = 666 x 1 + 203

We consider the new divisor 666 and the new remainder 203,and apply the division lemma to get

666 = 203 x 3 + 57

We consider the new divisor 203 and the new remainder 57,and apply the division lemma to get

203 = 57 x 3 + 32

We consider the new divisor 57 and the new remainder 32,and apply the division lemma to get

57 = 32 x 1 + 25

We consider the new divisor 32 and the new remainder 25,and apply the division lemma to get

32 = 25 x 1 + 7

We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get

25 = 7 x 3 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8544 and 1535 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(32,25) = HCF(57,32) = HCF(203,57) = HCF(666,203) = HCF(869,666) = HCF(1535,869) = HCF(8544,1535) .

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Frequently Asked Questions on HCF of 8544, 1535 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 8544, 1535?

Answer: HCF of 8544, 1535 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8544, 1535 using Euclid's Algorithm?

Answer: For arbitrary numbers 8544, 1535 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.