Highest Common Factor of 468, 725, 72 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 468, 725, 72 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 468, 725, 72 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 468, 725, 72 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 468, 725, 72 is 1.

HCF(468, 725, 72) = 1

HCF of 468, 725, 72 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 468, 725, 72 is 1.

Highest Common Factor of 468,725,72 using Euclid's algorithm

Highest Common Factor of 468,725,72 is 1

Step 1: Since 725 > 468, we apply the division lemma to 725 and 468, to get

725 = 468 x 1 + 257

Step 2: Since the reminder 468 ≠ 0, we apply division lemma to 257 and 468, to get

468 = 257 x 1 + 211

Step 3: We consider the new divisor 257 and the new remainder 211, and apply the division lemma to get

257 = 211 x 1 + 46

We consider the new divisor 211 and the new remainder 46,and apply the division lemma to get

211 = 46 x 4 + 27

We consider the new divisor 46 and the new remainder 27,and apply the division lemma to get

46 = 27 x 1 + 19

We consider the new divisor 27 and the new remainder 19,and apply the division lemma to get

27 = 19 x 1 + 8

We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get

19 = 8 x 2 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

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 468 and 725 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(46,27) = HCF(211,46) = HCF(257,211) = HCF(468,257) = HCF(725,468) .

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

Step 1: Since 72 > 1, we apply the division lemma to 72 and 1, to get

72 = 1 x 72 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 72 is 1

Notice that 1 = HCF(72,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 468, 725, 72 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 468, 725, 72?

Answer: HCF of 468, 725, 72 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 468, 725, 72 using Euclid's Algorithm?

Answer: For arbitrary numbers 468, 725, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.