Highest Common Factor of 542, 909, 540 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 542, 909, 540 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 542, 909, 540 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 542, 909, 540 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 542, 909, 540 is 1.

HCF(542, 909, 540) = 1

HCF of 542, 909, 540 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 542, 909, 540 is 1.

Highest Common Factor of 542,909,540 using Euclid's algorithm

Highest Common Factor of 542,909,540 is 1

Step 1: Since 909 > 542, we apply the division lemma to 909 and 542, to get

909 = 542 x 1 + 367

Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 367 and 542, to get

542 = 367 x 1 + 175

Step 3: We consider the new divisor 367 and the new remainder 175, and apply the division lemma to get

367 = 175 x 2 + 17

We consider the new divisor 175 and the new remainder 17,and apply the division lemma to get

175 = 17 x 10 + 5

We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get

17 = 5 x 3 + 2

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 542 and 909 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(175,17) = HCF(367,175) = HCF(542,367) = HCF(909,542) .

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

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

540 = 1 x 540 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 540 is 1

Notice that 1 = HCF(540,1) .

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Frequently Asked Questions on HCF of 542, 909, 540 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 542, 909, 540?

Answer: HCF of 542, 909, 540 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 542, 909, 540 using Euclid's Algorithm?

Answer: For arbitrary numbers 542, 909, 540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.