Highest Common Factor of 457, 745, 408 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, 745, 408 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 457, 745, 408 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, 745, 408 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, 745, 408 is 1.

HCF(457, 745, 408) = 1

HCF of 457, 745, 408 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, 745, 408 is 1.

Highest Common Factor of 457,745,408 using Euclid's algorithm

Highest Common Factor of 457,745,408 is 1

Step 1: Since 745 > 457, we apply the division lemma to 745 and 457, to get

745 = 457 x 1 + 288

Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 288 and 457, to get

457 = 288 x 1 + 169

Step 3: We consider the new divisor 288 and the new remainder 169, and apply the division lemma to get

288 = 169 x 1 + 119

We consider the new divisor 169 and the new remainder 119,and apply the division lemma to get

169 = 119 x 1 + 50

We consider the new divisor 119 and the new remainder 50,and apply the division lemma to get

119 = 50 x 2 + 19

We consider the new divisor 50 and the new remainder 19,and apply the division lemma to get

50 = 19 x 2 + 12

We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get

19 = 12 x 1 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 457 and 745 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(50,19) = HCF(119,50) = HCF(169,119) = HCF(288,169) = HCF(457,288) = HCF(745,457) .

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

Step 1: Since 408 > 1, we apply the division lemma to 408 and 1, to get

408 = 1 x 408 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 408 is 1

Notice that 1 = HCF(408,1) .

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Frequently Asked Questions on HCF of 457, 745, 408 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, 745, 408?

Answer: HCF of 457, 745, 408 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 457, 745, 408 using Euclid's Algorithm?

Answer: For arbitrary numbers 457, 745, 408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.