Highest Common Factor of 578, 806, 804 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 578, 806, 804 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 578, 806, 804 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 578, 806, 804 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 578, 806, 804 is 2.

HCF(578, 806, 804) = 2

HCF of 578, 806, 804 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 578, 806, 804 is 2.

Highest Common Factor of 578,806,804 using Euclid's algorithm

Highest Common Factor of 578,806,804 is 2

Step 1: Since 806 > 578, we apply the division lemma to 806 and 578, to get

806 = 578 x 1 + 228

Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 228 and 578, to get

578 = 228 x 2 + 122

Step 3: We consider the new divisor 228 and the new remainder 122, and apply the division lemma to get

228 = 122 x 1 + 106

We consider the new divisor 122 and the new remainder 106,and apply the division lemma to get

122 = 106 x 1 + 16

We consider the new divisor 106 and the new remainder 16,and apply the division lemma to get

106 = 16 x 6 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 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 578 and 806 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(106,16) = HCF(122,106) = HCF(228,122) = HCF(578,228) = HCF(806,578) .

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

Step 1: Since 804 > 2, we apply the division lemma to 804 and 2, to get

804 = 2 x 402 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 804 is 2

Notice that 2 = HCF(804,2) .

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Frequently Asked Questions on HCF of 578, 806, 804 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 578, 806, 804?

Answer: HCF of 578, 806, 804 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 578, 806, 804 using Euclid's Algorithm?

Answer: For arbitrary numbers 578, 806, 804 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.