Highest Common Factor of 540, 768, 685 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, 768, 685 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 540, 768, 685 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, 768, 685 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, 768, 685 is 1.

HCF(540, 768, 685) = 1

HCF of 540, 768, 685 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, 768, 685 is 1.

Highest Common Factor of 540,768,685 using Euclid's algorithm

Highest Common Factor of 540,768,685 is 1

Step 1: Since 768 > 540, we apply the division lemma to 768 and 540, to get

768 = 540 x 1 + 228

Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 228 and 540, to get

540 = 228 x 2 + 84

Step 3: We consider the new divisor 228 and the new remainder 84, and apply the division lemma to get

228 = 84 x 2 + 60

We consider the new divisor 84 and the new remainder 60,and apply the division lemma to get

84 = 60 x 1 + 24

We consider the new divisor 60 and the new remainder 24,and apply the division lemma to get

60 = 24 x 2 + 12

We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get

24 = 12 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 540 and 768 is 12

Notice that 12 = HCF(24,12) = HCF(60,24) = HCF(84,60) = HCF(228,84) = HCF(540,228) = HCF(768,540) .

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

Step 1: Since 685 > 12, we apply the division lemma to 685 and 12, to get

685 = 12 x 57 + 1

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 1 and 12, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 685 is 1

Notice that 1 = HCF(12,1) = HCF(685,12) .

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Frequently Asked Questions on HCF of 540, 768, 685 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, 768, 685?

Answer: HCF of 540, 768, 685 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 540, 768, 685 using Euclid's Algorithm?

Answer: For arbitrary numbers 540, 768, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.