Highest Common Factor of 7505, 5889 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 7505, 5889 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7505, 5889 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 7505, 5889 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 7505, 5889 is 1.

HCF(7505, 5889) = 1

HCF of 7505, 5889 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 7505, 5889 is 1.

Highest Common Factor of 7505,5889 using Euclid's algorithm

Highest Common Factor of 7505,5889 is 1

Step 1: Since 7505 > 5889, we apply the division lemma to 7505 and 5889, to get

7505 = 5889 x 1 + 1616

Step 2: Since the reminder 5889 ≠ 0, we apply division lemma to 1616 and 5889, to get

5889 = 1616 x 3 + 1041

Step 3: We consider the new divisor 1616 and the new remainder 1041, and apply the division lemma to get

1616 = 1041 x 1 + 575

We consider the new divisor 1041 and the new remainder 575,and apply the division lemma to get

1041 = 575 x 1 + 466

We consider the new divisor 575 and the new remainder 466,and apply the division lemma to get

575 = 466 x 1 + 109

We consider the new divisor 466 and the new remainder 109,and apply the division lemma to get

466 = 109 x 4 + 30

We consider the new divisor 109 and the new remainder 30,and apply the division lemma to get

109 = 30 x 3 + 19

We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get

30 = 19 x 1 + 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 7505 and 5889 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(109,30) = HCF(466,109) = HCF(575,466) = HCF(1041,575) = HCF(1616,1041) = HCF(5889,1616) = HCF(7505,5889) .

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Frequently Asked Questions on HCF of 7505, 5889 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 7505, 5889?

Answer: HCF of 7505, 5889 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7505, 5889 using Euclid's Algorithm?

Answer: For arbitrary numbers 7505, 5889 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.