Highest Common Factor of 5904, 8945 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 5904, 8945 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5904, 8945 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 5904, 8945 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 5904, 8945 is 1.

HCF(5904, 8945) = 1

HCF of 5904, 8945 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 5904, 8945 is 1.

Highest Common Factor of 5904,8945 using Euclid's algorithm

Highest Common Factor of 5904,8945 is 1

Step 1: Since 8945 > 5904, we apply the division lemma to 8945 and 5904, to get

8945 = 5904 x 1 + 3041

Step 2: Since the reminder 5904 ≠ 0, we apply division lemma to 3041 and 5904, to get

5904 = 3041 x 1 + 2863

Step 3: We consider the new divisor 3041 and the new remainder 2863, and apply the division lemma to get

3041 = 2863 x 1 + 178

We consider the new divisor 2863 and the new remainder 178,and apply the division lemma to get

2863 = 178 x 16 + 15

We consider the new divisor 178 and the new remainder 15,and apply the division lemma to get

178 = 15 x 11 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 5904 and 8945 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(178,15) = HCF(2863,178) = HCF(3041,2863) = HCF(5904,3041) = HCF(8945,5904) .

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Frequently Asked Questions on HCF of 5904, 8945 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 5904, 8945?

Answer: HCF of 5904, 8945 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5904, 8945 using Euclid's Algorithm?

Answer: For arbitrary numbers 5904, 8945 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.