Highest Common Factor of 7232, 6123 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 7232, 6123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7232, 6123 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 7232, 6123 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 7232, 6123 is 1.

HCF(7232, 6123) = 1

HCF of 7232, 6123 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 7232, 6123 is 1.

Highest Common Factor of 7232,6123 using Euclid's algorithm

Highest Common Factor of 7232,6123 is 1

Step 1: Since 7232 > 6123, we apply the division lemma to 7232 and 6123, to get

7232 = 6123 x 1 + 1109

Step 2: Since the reminder 6123 ≠ 0, we apply division lemma to 1109 and 6123, to get

6123 = 1109 x 5 + 578

Step 3: We consider the new divisor 1109 and the new remainder 578, and apply the division lemma to get

1109 = 578 x 1 + 531

We consider the new divisor 578 and the new remainder 531,and apply the division lemma to get

578 = 531 x 1 + 47

We consider the new divisor 531 and the new remainder 47,and apply the division lemma to get

531 = 47 x 11 + 14

We consider the new divisor 47 and the new remainder 14,and apply the division lemma to get

47 = 14 x 3 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 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 7232 and 6123 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(47,14) = HCF(531,47) = HCF(578,531) = HCF(1109,578) = HCF(6123,1109) = HCF(7232,6123) .

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Frequently Asked Questions on HCF of 7232, 6123 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 7232, 6123?

Answer: HCF of 7232, 6123 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7232, 6123 using Euclid's Algorithm?

Answer: For arbitrary numbers 7232, 6123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.