Highest Common Factor of 507, 724, 71 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 507, 724, 71 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 507, 724, 71 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 507, 724, 71 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 507, 724, 71 is 1.

HCF(507, 724, 71) = 1

HCF of 507, 724, 71 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 507, 724, 71 is 1.

Highest Common Factor of 507,724,71 using Euclid's algorithm

Highest Common Factor of 507,724,71 is 1

Step 1: Since 724 > 507, we apply the division lemma to 724 and 507, to get

724 = 507 x 1 + 217

Step 2: Since the reminder 507 ≠ 0, we apply division lemma to 217 and 507, to get

507 = 217 x 2 + 73

Step 3: We consider the new divisor 217 and the new remainder 73, and apply the division lemma to get

217 = 73 x 2 + 71

We consider the new divisor 73 and the new remainder 71,and apply the division lemma to get

73 = 71 x 1 + 2

We consider the new divisor 71 and the new remainder 2,and apply the division lemma to get

71 = 2 x 35 + 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 507 and 724 is 1

Notice that 1 = HCF(2,1) = HCF(71,2) = HCF(73,71) = HCF(217,73) = HCF(507,217) = HCF(724,507) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 71 > 1, we apply the division lemma to 71 and 1, to get

71 = 1 x 71 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 71 is 1

Notice that 1 = HCF(71,1) .

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Frequently Asked Questions on HCF of 507, 724, 71 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 507, 724, 71?

Answer: HCF of 507, 724, 71 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 507, 724, 71 using Euclid's Algorithm?

Answer: For arbitrary numbers 507, 724, 71 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.