Highest Common Factor of 741, 542, 683 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 741, 542, 683 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 741, 542, 683 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 741, 542, 683 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 741, 542, 683 is 1.

HCF(741, 542, 683) = 1

HCF of 741, 542, 683 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 741, 542, 683 is 1.

Highest Common Factor of 741,542,683 using Euclid's algorithm

Highest Common Factor of 741,542,683 is 1

Step 1: Since 741 > 542, we apply the division lemma to 741 and 542, to get

741 = 542 x 1 + 199

Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 199 and 542, to get

542 = 199 x 2 + 144

Step 3: We consider the new divisor 199 and the new remainder 144, and apply the division lemma to get

199 = 144 x 1 + 55

We consider the new divisor 144 and the new remainder 55,and apply the division lemma to get

144 = 55 x 2 + 34

We consider the new divisor 55 and the new remainder 34,and apply the division lemma to get

55 = 34 x 1 + 21

We consider the new divisor 34 and the new remainder 21,and apply the division lemma to get

34 = 21 x 1 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 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 741 and 542 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(34,21) = HCF(55,34) = HCF(144,55) = HCF(199,144) = HCF(542,199) = HCF(741,542) .

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

Step 1: Since 683 > 1, we apply the division lemma to 683 and 1, to get

683 = 1 x 683 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 683 is 1

Notice that 1 = HCF(683,1) .

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Frequently Asked Questions on HCF of 741, 542, 683 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 741, 542, 683?

Answer: HCF of 741, 542, 683 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 741, 542, 683 using Euclid's Algorithm?

Answer: For arbitrary numbers 741, 542, 683 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.