Highest Common Factor of 457, 264, 738 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, 264, 738 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 457, 264, 738 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, 264, 738 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, 264, 738 is 1.

HCF(457, 264, 738) = 1

HCF of 457, 264, 738 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, 264, 738 is 1.

Highest Common Factor of 457,264,738 using Euclid's algorithm

Highest Common Factor of 457,264,738 is 1

Step 1: Since 457 > 264, we apply the division lemma to 457 and 264, to get

457 = 264 x 1 + 193

Step 2: Since the reminder 264 ≠ 0, we apply division lemma to 193 and 264, to get

264 = 193 x 1 + 71

Step 3: We consider the new divisor 193 and the new remainder 71, and apply the division lemma to get

193 = 71 x 2 + 51

We consider the new divisor 71 and the new remainder 51,and apply the division lemma to get

71 = 51 x 1 + 20

We consider the new divisor 51 and the new remainder 20,and apply the division lemma to get

51 = 20 x 2 + 11

We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get

20 = 11 x 1 + 9

We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get

11 = 9 x 1 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 264 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(51,20) = HCF(71,51) = HCF(193,71) = HCF(264,193) = HCF(457,264) .

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

Step 1: Since 738 > 1, we apply the division lemma to 738 and 1, to get

738 = 1 x 738 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 738 is 1

Notice that 1 = HCF(738,1) .

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Frequently Asked Questions on HCF of 457, 264, 738 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, 264, 738?

Answer: HCF of 457, 264, 738 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 457, 264, 738 using Euclid's Algorithm?

Answer: For arbitrary numbers 457, 264, 738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.