Highest Common Factor of 743, 605, 750 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, 605, 750 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 743, 605, 750 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, 605, 750 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, 605, 750 is 1.

HCF(743, 605, 750) = 1

HCF of 743, 605, 750 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, 605, 750 is 1.

Highest Common Factor of 743,605,750 using Euclid's algorithm

Highest Common Factor of 743,605,750 is 1

Step 1: Since 743 > 605, we apply the division lemma to 743 and 605, to get

743 = 605 x 1 + 138

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 138 and 605, to get

605 = 138 x 4 + 53

Step 3: We consider the new divisor 138 and the new remainder 53, and apply the division lemma to get

138 = 53 x 2 + 32

We consider the new divisor 53 and the new remainder 32,and apply the division lemma to get

53 = 32 x 1 + 21

We consider the new divisor 32 and the new remainder 21,and apply the division lemma to get

32 = 21 x 1 + 11

We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get

21 = 11 x 1 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 743 and 605 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) = HCF(53,32) = HCF(138,53) = HCF(605,138) = HCF(743,605) .

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

Step 1: Since 750 > 1, we apply the division lemma to 750 and 1, to get

750 = 1 x 750 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 750 is 1

Notice that 1 = HCF(750,1) .

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Frequently Asked Questions on HCF of 743, 605, 750 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, 605, 750?

Answer: HCF of 743, 605, 750 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 743, 605, 750 using Euclid's Algorithm?

Answer: For arbitrary numbers 743, 605, 750 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.