Highest Common Factor of 8500, 4754, 90112 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 8500, 4754, 90112 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 8500, 4754, 90112 is 2 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 8500, 4754, 90112 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 8500, 4754, 90112 is 2.

HCF(8500, 4754, 90112) = 2

HCF of 8500, 4754, 90112 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 8500, 4754, 90112 is 2.

Highest Common Factor of 8500,4754,90112 using Euclid's algorithm

Highest Common Factor of 8500,4754,90112 is 2

Step 1: Since 8500 > 4754, we apply the division lemma to 8500 and 4754, to get

8500 = 4754 x 1 + 3746

Step 2: Since the reminder 4754 ≠ 0, we apply division lemma to 3746 and 4754, to get

4754 = 3746 x 1 + 1008

Step 3: We consider the new divisor 3746 and the new remainder 1008, and apply the division lemma to get

3746 = 1008 x 3 + 722

We consider the new divisor 1008 and the new remainder 722,and apply the division lemma to get

1008 = 722 x 1 + 286

We consider the new divisor 722 and the new remainder 286,and apply the division lemma to get

722 = 286 x 2 + 150

We consider the new divisor 286 and the new remainder 150,and apply the division lemma to get

286 = 150 x 1 + 136

We consider the new divisor 150 and the new remainder 136,and apply the division lemma to get

150 = 136 x 1 + 14

We consider the new divisor 136 and the new remainder 14,and apply the division lemma to get

136 = 14 x 9 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8500 and 4754 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(136,14) = HCF(150,136) = HCF(286,150) = HCF(722,286) = HCF(1008,722) = HCF(3746,1008) = HCF(4754,3746) = HCF(8500,4754) .

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

Step 1: Since 90112 > 2, we apply the division lemma to 90112 and 2, to get

90112 = 2 x 45056 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 90112 is 2

Notice that 2 = HCF(90112,2) .

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Frequently Asked Questions on HCF of 8500, 4754, 90112 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 8500, 4754, 90112?

Answer: HCF of 8500, 4754, 90112 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8500, 4754, 90112 using Euclid's Algorithm?

Answer: For arbitrary numbers 8500, 4754, 90112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.