Highest Common Factor of 725, 530, 478 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 725, 530, 478 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 725, 530, 478 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 725, 530, 478 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 725, 530, 478 is 1.

HCF(725, 530, 478) = 1

HCF of 725, 530, 478 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 725, 530, 478 is 1.

Highest Common Factor of 725,530,478 using Euclid's algorithm

Highest Common Factor of 725,530,478 is 1

Step 1: Since 725 > 530, we apply the division lemma to 725 and 530, to get

725 = 530 x 1 + 195

Step 2: Since the reminder 530 ≠ 0, we apply division lemma to 195 and 530, to get

530 = 195 x 2 + 140

Step 3: We consider the new divisor 195 and the new remainder 140, and apply the division lemma to get

195 = 140 x 1 + 55

We consider the new divisor 140 and the new remainder 55,and apply the division lemma to get

140 = 55 x 2 + 30

We consider the new divisor 55 and the new remainder 30,and apply the division lemma to get

55 = 30 x 1 + 25

We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get

30 = 25 x 1 + 5

We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 725 and 530 is 5

Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(55,30) = HCF(140,55) = HCF(195,140) = HCF(530,195) = HCF(725,530) .

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

Step 1: Since 478 > 5, we apply the division lemma to 478 and 5, to get

478 = 5 x 95 + 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 478 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(478,5) .

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Frequently Asked Questions on HCF of 725, 530, 478 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 725, 530, 478?

Answer: HCF of 725, 530, 478 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 725, 530, 478 using Euclid's Algorithm?

Answer: For arbitrary numbers 725, 530, 478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.