Highest Common Factor of 509, 724 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 509, 724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 509, 724 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 509, 724 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 509, 724 is 1.

HCF(509, 724) = 1

HCF of 509, 724 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 509, 724 is 1.

Highest Common Factor of 509,724 using Euclid's algorithm

Highest Common Factor of 509,724 is 1

Step 1: Since 724 > 509, we apply the division lemma to 724 and 509, to get

724 = 509 x 1 + 215

Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 215 and 509, to get

509 = 215 x 2 + 79

Step 3: We consider the new divisor 215 and the new remainder 79, and apply the division lemma to get

215 = 79 x 2 + 57

We consider the new divisor 79 and the new remainder 57,and apply the division lemma to get

79 = 57 x 1 + 22

We consider the new divisor 57 and the new remainder 22,and apply the division lemma to get

57 = 22 x 2 + 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 509 and 724 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(57,22) = HCF(79,57) = HCF(215,79) = HCF(509,215) = HCF(724,509) .

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Frequently Asked Questions on HCF of 509, 724 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 509, 724?

Answer: HCF of 509, 724 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 509, 724 using Euclid's Algorithm?

Answer: For arbitrary numbers 509, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.