Highest Common Factor of 4003, 5040 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 4003, 5040 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 4003, 5040 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 4003, 5040 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 4003, 5040 is 1.

HCF(4003, 5040) = 1

HCF of 4003, 5040 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 4003, 5040 is 1.

Highest Common Factor of 4003,5040 using Euclid's algorithm

Highest Common Factor of 4003,5040 is 1

Step 1: Since 5040 > 4003, we apply the division lemma to 5040 and 4003, to get

5040 = 4003 x 1 + 1037

Step 2: Since the reminder 4003 ≠ 0, we apply division lemma to 1037 and 4003, to get

4003 = 1037 x 3 + 892

Step 3: We consider the new divisor 1037 and the new remainder 892, and apply the division lemma to get

1037 = 892 x 1 + 145

We consider the new divisor 892 and the new remainder 145,and apply the division lemma to get

892 = 145 x 6 + 22

We consider the new divisor 145 and the new remainder 22,and apply the division lemma to get

145 = 22 x 6 + 13

We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get

22 = 13 x 1 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4003 and 5040 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(145,22) = HCF(892,145) = HCF(1037,892) = HCF(4003,1037) = HCF(5040,4003) .

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Frequently Asked Questions on HCF of 4003, 5040 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 4003, 5040?

Answer: HCF of 4003, 5040 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 4003, 5040 using Euclid's Algorithm?

Answer: For arbitrary numbers 4003, 5040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.