Highest Common Factor of 800, 586, 16 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 800, 586, 16 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 800, 586, 16 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 800, 586, 16 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 800, 586, 16 is 2.

HCF(800, 586, 16) = 2

HCF of 800, 586, 16 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 800, 586, 16 is 2.

Highest Common Factor of 800,586,16 using Euclid's algorithm

Highest Common Factor of 800,586,16 is 2

Step 1: Since 800 > 586, we apply the division lemma to 800 and 586, to get

800 = 586 x 1 + 214

Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 214 and 586, to get

586 = 214 x 2 + 158

Step 3: We consider the new divisor 214 and the new remainder 158, and apply the division lemma to get

214 = 158 x 1 + 56

We consider the new divisor 158 and the new remainder 56,and apply the division lemma to get

158 = 56 x 2 + 46

We consider the new divisor 56 and the new remainder 46,and apply the division lemma to get

56 = 46 x 1 + 10

We consider the new divisor 46 and the new remainder 10,and apply the division lemma to get

46 = 10 x 4 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 800 and 586 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(46,10) = HCF(56,46) = HCF(158,56) = HCF(214,158) = HCF(586,214) = HCF(800,586) .

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

Step 1: Since 16 > 2, we apply the division lemma to 16 and 2, to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 16 is 2

Notice that 2 = HCF(16,2) .

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Frequently Asked Questions on HCF of 800, 586, 16 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 800, 586, 16?

Answer: HCF of 800, 586, 16 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 800, 586, 16 using Euclid's Algorithm?

Answer: For arbitrary numbers 800, 586, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.