Highest Common Factor of 7135, 2004 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 7135, 2004 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7135, 2004 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 7135, 2004 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 7135, 2004 is 1.

HCF(7135, 2004) = 1

HCF of 7135, 2004 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 7135, 2004 is 1.

Highest Common Factor of 7135,2004 using Euclid's algorithm

Highest Common Factor of 7135,2004 is 1

Step 1: Since 7135 > 2004, we apply the division lemma to 7135 and 2004, to get

7135 = 2004 x 3 + 1123

Step 2: Since the reminder 2004 ≠ 0, we apply division lemma to 1123 and 2004, to get

2004 = 1123 x 1 + 881

Step 3: We consider the new divisor 1123 and the new remainder 881, and apply the division lemma to get

1123 = 881 x 1 + 242

We consider the new divisor 881 and the new remainder 242,and apply the division lemma to get

881 = 242 x 3 + 155

We consider the new divisor 242 and the new remainder 155,and apply the division lemma to get

242 = 155 x 1 + 87

We consider the new divisor 155 and the new remainder 87,and apply the division lemma to get

155 = 87 x 1 + 68

We consider the new divisor 87 and the new remainder 68,and apply the division lemma to get

87 = 68 x 1 + 19

We consider the new divisor 68 and the new remainder 19,and apply the division lemma to get

68 = 19 x 3 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 7135 and 2004 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(68,19) = HCF(87,68) = HCF(155,87) = HCF(242,155) = HCF(881,242) = HCF(1123,881) = HCF(2004,1123) = HCF(7135,2004) .

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Frequently Asked Questions on HCF of 7135, 2004 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 7135, 2004?

Answer: HCF of 7135, 2004 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7135, 2004 using Euclid's Algorithm?

Answer: For arbitrary numbers 7135, 2004 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.