Highest Common Factor of 576, 804, 353 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 576, 804, 353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 576, 804, 353 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 576, 804, 353 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 576, 804, 353 is 1.

HCF(576, 804, 353) = 1

HCF of 576, 804, 353 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 576, 804, 353 is 1.

Highest Common Factor of 576,804,353 using Euclid's algorithm

Highest Common Factor of 576,804,353 is 1

Step 1: Since 804 > 576, we apply the division lemma to 804 and 576, to get

804 = 576 x 1 + 228

Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 228 and 576, to get

576 = 228 x 2 + 120

Step 3: We consider the new divisor 228 and the new remainder 120, and apply the division lemma to get

228 = 120 x 1 + 108

We consider the new divisor 120 and the new remainder 108,and apply the division lemma to get

120 = 108 x 1 + 12

We consider the new divisor 108 and the new remainder 12,and apply the division lemma to get

108 = 12 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 576 and 804 is 12

Notice that 12 = HCF(108,12) = HCF(120,108) = HCF(228,120) = HCF(576,228) = HCF(804,576) .

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

Step 1: Since 353 > 12, we apply the division lemma to 353 and 12, to get

353 = 12 x 29 + 5

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 5 and 12, to get

12 = 5 x 2 + 2

Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 353 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(353,12) .

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Frequently Asked Questions on HCF of 576, 804, 353 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 576, 804, 353?

Answer: HCF of 576, 804, 353 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 576, 804, 353 using Euclid's Algorithm?

Answer: For arbitrary numbers 576, 804, 353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.