Highest Common Factor of 1538, 5045 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 1538, 5045 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1538, 5045 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 1538, 5045 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 1538, 5045 is 1.

HCF(1538, 5045) = 1

HCF of 1538, 5045 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 1538, 5045 is 1.

Highest Common Factor of 1538,5045 using Euclid's algorithm

Highest Common Factor of 1538,5045 is 1

Step 1: Since 5045 > 1538, we apply the division lemma to 5045 and 1538, to get

5045 = 1538 x 3 + 431

Step 2: Since the reminder 1538 ≠ 0, we apply division lemma to 431 and 1538, to get

1538 = 431 x 3 + 245

Step 3: We consider the new divisor 431 and the new remainder 245, and apply the division lemma to get

431 = 245 x 1 + 186

We consider the new divisor 245 and the new remainder 186,and apply the division lemma to get

245 = 186 x 1 + 59

We consider the new divisor 186 and the new remainder 59,and apply the division lemma to get

186 = 59 x 3 + 9

We consider the new divisor 59 and the new remainder 9,and apply the division lemma to get

59 = 9 x 6 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 1538 and 5045 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(59,9) = HCF(186,59) = HCF(245,186) = HCF(431,245) = HCF(1538,431) = HCF(5045,1538) .

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Frequently Asked Questions on HCF of 1538, 5045 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 1538, 5045?

Answer: HCF of 1538, 5045 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1538, 5045 using Euclid's Algorithm?

Answer: For arbitrary numbers 1538, 5045 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.