Highest Common Factor of 3004, 7127 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 3004, 7127 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3004, 7127 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 3004, 7127 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 3004, 7127 is 1.

HCF(3004, 7127) = 1

HCF of 3004, 7127 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 3004, 7127 is 1.

Highest Common Factor of 3004,7127 using Euclid's algorithm

Highest Common Factor of 3004,7127 is 1

Step 1: Since 7127 > 3004, we apply the division lemma to 7127 and 3004, to get

7127 = 3004 x 2 + 1119

Step 2: Since the reminder 3004 ≠ 0, we apply division lemma to 1119 and 3004, to get

3004 = 1119 x 2 + 766

Step 3: We consider the new divisor 1119 and the new remainder 766, and apply the division lemma to get

1119 = 766 x 1 + 353

We consider the new divisor 766 and the new remainder 353,and apply the division lemma to get

766 = 353 x 2 + 60

We consider the new divisor 353 and the new remainder 60,and apply the division lemma to get

353 = 60 x 5 + 53

We consider the new divisor 60 and the new remainder 53,and apply the division lemma to get

60 = 53 x 1 + 7

We consider the new divisor 53 and the new remainder 7,and apply the division lemma to get

53 = 7 x 7 + 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 3004 and 7127 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(53,7) = HCF(60,53) = HCF(353,60) = HCF(766,353) = HCF(1119,766) = HCF(3004,1119) = HCF(7127,3004) .

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Frequently Asked Questions on HCF of 3004, 7127 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 3004, 7127?

Answer: HCF of 3004, 7127 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3004, 7127 using Euclid's Algorithm?

Answer: For arbitrary numbers 3004, 7127 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.