Highest Common Factor of 459, 540, 46 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 459, 540, 46 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 459, 540, 46 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 459, 540, 46 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 459, 540, 46 is 1.

HCF(459, 540, 46) = 1

HCF of 459, 540, 46 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 459, 540, 46 is 1.

Highest Common Factor of 459,540,46 using Euclid's algorithm

Highest Common Factor of 459,540,46 is 1

Step 1: Since 540 > 459, we apply the division lemma to 540 and 459, to get

540 = 459 x 1 + 81

Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 81 and 459, to get

459 = 81 x 5 + 54

Step 3: We consider the new divisor 81 and the new remainder 54, and apply the division lemma to get

81 = 54 x 1 + 27

We consider the new divisor 54 and the new remainder 27, and apply the division lemma to get

54 = 27 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 459 and 540 is 27

Notice that 27 = HCF(54,27) = HCF(81,54) = HCF(459,81) = HCF(540,459) .

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

Step 1: Since 46 > 27, we apply the division lemma to 46 and 27, to get

46 = 27 x 1 + 19

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 19 and 27, to get

27 = 19 x 1 + 8

Step 3: We consider the new divisor 19 and the new remainder 8, and apply the division lemma to get

19 = 8 x 2 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

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

3 = 2 x 1 + 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 27 and 46 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(46,27) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 459, 540, 46 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 459, 540, 46?

Answer: HCF of 459, 540, 46 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 459, 540, 46 using Euclid's Algorithm?

Answer: For arbitrary numbers 459, 540, 46 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.