Highest Common Factor of 745, 540, 878 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 745, 540, 878 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 745, 540, 878 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 745, 540, 878 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 745, 540, 878 is 1.

HCF(745, 540, 878) = 1

HCF of 745, 540, 878 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 745, 540, 878 is 1.

Highest Common Factor of 745,540,878 using Euclid's algorithm

Highest Common Factor of 745,540,878 is 1

Step 1: Since 745 > 540, we apply the division lemma to 745 and 540, to get

745 = 540 x 1 + 205

Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 205 and 540, to get

540 = 205 x 2 + 130

Step 3: We consider the new divisor 205 and the new remainder 130, and apply the division lemma to get

205 = 130 x 1 + 75

We consider the new divisor 130 and the new remainder 75,and apply the division lemma to get

130 = 75 x 1 + 55

We consider the new divisor 75 and the new remainder 55,and apply the division lemma to get

75 = 55 x 1 + 20

We consider the new divisor 55 and the new remainder 20,and apply the division lemma to get

55 = 20 x 2 + 15

We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get

20 = 15 x 1 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 745 and 540 is 5

Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(55,20) = HCF(75,55) = HCF(130,75) = HCF(205,130) = HCF(540,205) = HCF(745,540) .

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

Step 1: Since 878 > 5, we apply the division lemma to 878 and 5, to get

878 = 5 x 175 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 878 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(878,5) .

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Frequently Asked Questions on HCF of 745, 540, 878 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 745, 540, 878?

Answer: HCF of 745, 540, 878 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 745, 540, 878 using Euclid's Algorithm?

Answer: For arbitrary numbers 745, 540, 878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.