Highest Common Factor of 457, 289, 605 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 457, 289, 605 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 457, 289, 605 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 457, 289, 605 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 457, 289, 605 is 1.

HCF(457, 289, 605) = 1

HCF of 457, 289, 605 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 457, 289, 605 is 1.

Highest Common Factor of 457,289,605 using Euclid's algorithm

Highest Common Factor of 457,289,605 is 1

Step 1: Since 457 > 289, we apply the division lemma to 457 and 289, to get

457 = 289 x 1 + 168

Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 168 and 289, to get

289 = 168 x 1 + 121

Step 3: We consider the new divisor 168 and the new remainder 121, and apply the division lemma to get

168 = 121 x 1 + 47

We consider the new divisor 121 and the new remainder 47,and apply the division lemma to get

121 = 47 x 2 + 27

We consider the new divisor 47 and the new remainder 27,and apply the division lemma to get

47 = 27 x 1 + 20

We consider the new divisor 27 and the new remainder 20,and apply the division lemma to get

27 = 20 x 1 + 7

We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get

20 = 7 x 2 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 289 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(47,27) = HCF(121,47) = HCF(168,121) = HCF(289,168) = HCF(457,289) .

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

Step 1: Since 605 > 1, we apply the division lemma to 605 and 1, to get

605 = 1 x 605 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 605 is 1

Notice that 1 = HCF(605,1) .

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Frequently Asked Questions on HCF of 457, 289, 605 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 457, 289, 605?

Answer: HCF of 457, 289, 605 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 457, 289, 605 using Euclid's Algorithm?

Answer: For arbitrary numbers 457, 289, 605 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.