Highest Common Factor of 473, 745, 440 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 473, 745, 440 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 473, 745, 440 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 473, 745, 440 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 473, 745, 440 is 1.

HCF(473, 745, 440) = 1

HCF of 473, 745, 440 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 473, 745, 440 is 1.

Highest Common Factor of 473,745,440 using Euclid's algorithm

Highest Common Factor of 473,745,440 is 1

Step 1: Since 745 > 473, we apply the division lemma to 745 and 473, to get

745 = 473 x 1 + 272

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 272 and 473, to get

473 = 272 x 1 + 201

Step 3: We consider the new divisor 272 and the new remainder 201, and apply the division lemma to get

272 = 201 x 1 + 71

We consider the new divisor 201 and the new remainder 71,and apply the division lemma to get

201 = 71 x 2 + 59

We consider the new divisor 71 and the new remainder 59,and apply the division lemma to get

71 = 59 x 1 + 12

We consider the new divisor 59 and the new remainder 12,and apply the division lemma to get

59 = 12 x 4 + 11

We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get

12 = 11 x 1 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 473 and 745 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(59,12) = HCF(71,59) = HCF(201,71) = HCF(272,201) = HCF(473,272) = HCF(745,473) .

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

Step 1: Since 440 > 1, we apply the division lemma to 440 and 1, to get

440 = 1 x 440 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 440 is 1

Notice that 1 = HCF(440,1) .

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Frequently Asked Questions on HCF of 473, 745, 440 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 473, 745, 440?

Answer: HCF of 473, 745, 440 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 473, 745, 440 using Euclid's Algorithm?

Answer: For arbitrary numbers 473, 745, 440 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.