Highest Common Factor of 540, 591, 350 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 540, 591, 350 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 540, 591, 350 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 540, 591, 350 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 540, 591, 350 is 1.

HCF(540, 591, 350) = 1

HCF of 540, 591, 350 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 540, 591, 350 is 1.

Highest Common Factor of 540,591,350 using Euclid's algorithm

Highest Common Factor of 540,591,350 is 1

Step 1: Since 591 > 540, we apply the division lemma to 591 and 540, to get

591 = 540 x 1 + 51

Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 51 and 540, to get

540 = 51 x 10 + 30

Step 3: We consider the new divisor 51 and the new remainder 30, and apply the division lemma to get

51 = 30 x 1 + 21

We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get

30 = 21 x 1 + 9

We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get

21 = 9 x 2 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 540 and 591 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(51,30) = HCF(540,51) = HCF(591,540) .

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

Step 1: Since 350 > 3, we apply the division lemma to 350 and 3, to get

350 = 3 x 116 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 350 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(350,3) .

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Frequently Asked Questions on HCF of 540, 591, 350 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 540, 591, 350?

Answer: HCF of 540, 591, 350 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 540, 591, 350 using Euclid's Algorithm?

Answer: For arbitrary numbers 540, 591, 350 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.