Highest Common Factor of 903, 560, 572 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 903, 560, 572 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 903, 560, 572 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 903, 560, 572 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 903, 560, 572 is 1.

HCF(903, 560, 572) = 1

HCF of 903, 560, 572 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 903, 560, 572 is 1.

Highest Common Factor of 903,560,572 using Euclid's algorithm

Highest Common Factor of 903,560,572 is 1

Step 1: Since 903 > 560, we apply the division lemma to 903 and 560, to get

903 = 560 x 1 + 343

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 343 and 560, to get

560 = 343 x 1 + 217

Step 3: We consider the new divisor 343 and the new remainder 217, and apply the division lemma to get

343 = 217 x 1 + 126

We consider the new divisor 217 and the new remainder 126,and apply the division lemma to get

217 = 126 x 1 + 91

We consider the new divisor 126 and the new remainder 91,and apply the division lemma to get

126 = 91 x 1 + 35

We consider the new divisor 91 and the new remainder 35,and apply the division lemma to get

91 = 35 x 2 + 21

We consider the new divisor 35 and the new remainder 21,and apply the division lemma to get

35 = 21 x 1 + 14

We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get

21 = 14 x 1 + 7

We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get

14 = 7 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 903 and 560 is 7

Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(35,21) = HCF(91,35) = HCF(126,91) = HCF(217,126) = HCF(343,217) = HCF(560,343) = HCF(903,560) .

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

Step 1: Since 572 > 7, we apply the division lemma to 572 and 7, to get

572 = 7 x 81 + 5

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 5 and 7, to get

7 = 5 x 1 + 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 7 and 572 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(572,7) .

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Frequently Asked Questions on HCF of 903, 560, 572 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 903, 560, 572?

Answer: HCF of 903, 560, 572 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 903, 560, 572 using Euclid's Algorithm?

Answer: For arbitrary numbers 903, 560, 572 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.