Highest Common Factor of 508, 737 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 508, 737 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 508, 737 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 508, 737 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 508, 737 is 1.

HCF(508, 737) = 1

HCF of 508, 737 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 508, 737 is 1.

Highest Common Factor of 508,737 using Euclid's algorithm

Highest Common Factor of 508,737 is 1

Step 1: Since 737 > 508, we apply the division lemma to 737 and 508, to get

737 = 508 x 1 + 229

Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 229 and 508, to get

508 = 229 x 2 + 50

Step 3: We consider the new divisor 229 and the new remainder 50, and apply the division lemma to get

229 = 50 x 4 + 29

We consider the new divisor 50 and the new remainder 29,and apply the division lemma to get

50 = 29 x 1 + 21

We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get

29 = 21 x 1 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 508 and 737 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(50,29) = HCF(229,50) = HCF(508,229) = HCF(737,508) .

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Frequently Asked Questions on HCF of 508, 737 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 508, 737?

Answer: HCF of 508, 737 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 508, 737 using Euclid's Algorithm?

Answer: For arbitrary numbers 508, 737 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.