Highest Common Factor of 523, 8832, 7243 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 523, 8832, 7243 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 8832, 7243 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 523, 8832, 7243 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 523, 8832, 7243 is 1.

HCF(523, 8832, 7243) = 1

HCF of 523, 8832, 7243 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 523, 8832, 7243 is 1.

Highest Common Factor of 523,8832,7243 using Euclid's algorithm

Highest Common Factor of 523,8832,7243 is 1

Step 1: Since 8832 > 523, we apply the division lemma to 8832 and 523, to get

8832 = 523 x 16 + 464

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 464 and 523, to get

523 = 464 x 1 + 59

Step 3: We consider the new divisor 464 and the new remainder 59, and apply the division lemma to get

464 = 59 x 7 + 51

We consider the new divisor 59 and the new remainder 51,and apply the division lemma to get

59 = 51 x 1 + 8

We consider the new divisor 51 and the new remainder 8,and apply the division lemma to get

51 = 8 x 6 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 523 and 8832 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(51,8) = HCF(59,51) = HCF(464,59) = HCF(523,464) = HCF(8832,523) .

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

Step 1: Since 7243 > 1, we apply the division lemma to 7243 and 1, to get

7243 = 1 x 7243 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7243 is 1

Notice that 1 = HCF(7243,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 523, 8832, 7243 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 523, 8832, 7243?

Answer: HCF of 523, 8832, 7243 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 8832, 7243 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 8832, 7243 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.