Highest Common Factor of 7523, 4176, 11500 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 7523, 4176, 11500 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7523, 4176, 11500 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 7523, 4176, 11500 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 7523, 4176, 11500 is 1.

HCF(7523, 4176, 11500) = 1

HCF of 7523, 4176, 11500 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 7523, 4176, 11500 is 1.

Highest Common Factor of 7523,4176,11500 using Euclid's algorithm

Highest Common Factor of 7523,4176,11500 is 1

Step 1: Since 7523 > 4176, we apply the division lemma to 7523 and 4176, to get

7523 = 4176 x 1 + 3347

Step 2: Since the reminder 4176 ≠ 0, we apply division lemma to 3347 and 4176, to get

4176 = 3347 x 1 + 829

Step 3: We consider the new divisor 3347 and the new remainder 829, and apply the division lemma to get

3347 = 829 x 4 + 31

We consider the new divisor 829 and the new remainder 31,and apply the division lemma to get

829 = 31 x 26 + 23

We consider the new divisor 31 and the new remainder 23,and apply the division lemma to get

31 = 23 x 1 + 8

We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get

23 = 8 x 2 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7523 and 4176 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(31,23) = HCF(829,31) = HCF(3347,829) = HCF(4176,3347) = HCF(7523,4176) .

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

Step 1: Since 11500 > 1, we apply the division lemma to 11500 and 1, to get

11500 = 1 x 11500 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 11500 is 1

Notice that 1 = HCF(11500,1) .

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Frequently Asked Questions on HCF of 7523, 4176, 11500 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 7523, 4176, 11500?

Answer: HCF of 7523, 4176, 11500 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7523, 4176, 11500 using Euclid's Algorithm?

Answer: For arbitrary numbers 7523, 4176, 11500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.