Highest Common Factor of 540, 752, 960 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, 752, 960 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 540, 752, 960 is 4 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, 752, 960 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, 752, 960 is 4.

HCF(540, 752, 960) = 4

HCF of 540, 752, 960 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, 752, 960 is 4.

Highest Common Factor of 540,752,960 using Euclid's algorithm

Highest Common Factor of 540,752,960 is 4

Step 1: Since 752 > 540, we apply the division lemma to 752 and 540, to get

752 = 540 x 1 + 212

Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 212 and 540, to get

540 = 212 x 2 + 116

Step 3: We consider the new divisor 212 and the new remainder 116, and apply the division lemma to get

212 = 116 x 1 + 96

We consider the new divisor 116 and the new remainder 96,and apply the division lemma to get

116 = 96 x 1 + 20

We consider the new divisor 96 and the new remainder 20,and apply the division lemma to get

96 = 20 x 4 + 16

We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get

20 = 16 x 1 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 540 and 752 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(96,20) = HCF(116,96) = HCF(212,116) = HCF(540,212) = HCF(752,540) .

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

Step 1: Since 960 > 4, we apply the division lemma to 960 and 4, to get

960 = 4 x 240 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 960 is 4

Notice that 4 = HCF(960,4) .

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Frequently Asked Questions on HCF of 540, 752, 960 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, 752, 960?

Answer: HCF of 540, 752, 960 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 540, 752, 960 using Euclid's Algorithm?

Answer: For arbitrary numbers 540, 752, 960 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.