Highest Common Factor of 743, 440, 508 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 743, 440, 508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 743, 440, 508 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 743, 440, 508 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 743, 440, 508 is 1.

HCF(743, 440, 508) = 1

HCF of 743, 440, 508 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 743, 440, 508 is 1.

Highest Common Factor of 743,440,508 using Euclid's algorithm

Highest Common Factor of 743,440,508 is 1

Step 1: Since 743 > 440, we apply the division lemma to 743 and 440, to get

743 = 440 x 1 + 303

Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 303 and 440, to get

440 = 303 x 1 + 137

Step 3: We consider the new divisor 303 and the new remainder 137, and apply the division lemma to get

303 = 137 x 2 + 29

We consider the new divisor 137 and the new remainder 29,and apply the division lemma to get

137 = 29 x 4 + 21

We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get

29 = 21 x 1 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 743 and 440 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(137,29) = HCF(303,137) = HCF(440,303) = HCF(743,440) .

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

Step 1: Since 508 > 1, we apply the division lemma to 508 and 1, to get

508 = 1 x 508 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 508 is 1

Notice that 1 = HCF(508,1) .

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Frequently Asked Questions on HCF of 743, 440, 508 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 743, 440, 508?

Answer: HCF of 743, 440, 508 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 743, 440, 508 using Euclid's Algorithm?

Answer: For arbitrary numbers 743, 440, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.