Highest Common Factor of 747, 542 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 747, 542 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 747, 542 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 747, 542 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 747, 542 is 1.

HCF(747, 542) = 1

HCF of 747, 542 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 747, 542 is 1.

Highest Common Factor of 747,542 using Euclid's algorithm

Highest Common Factor of 747,542 is 1

Step 1: Since 747 > 542, we apply the division lemma to 747 and 542, to get

747 = 542 x 1 + 205

Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 205 and 542, to get

542 = 205 x 2 + 132

Step 3: We consider the new divisor 205 and the new remainder 132, and apply the division lemma to get

205 = 132 x 1 + 73

We consider the new divisor 132 and the new remainder 73,and apply the division lemma to get

132 = 73 x 1 + 59

We consider the new divisor 73 and the new remainder 59,and apply the division lemma to get

73 = 59 x 1 + 14

We consider the new divisor 59 and the new remainder 14,and apply the division lemma to get

59 = 14 x 4 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 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 747 and 542 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(59,14) = HCF(73,59) = HCF(132,73) = HCF(205,132) = HCF(542,205) = HCF(747,542) .

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Frequently Asked Questions on HCF of 747, 542 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 747, 542?

Answer: HCF of 747, 542 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 747, 542 using Euclid's Algorithm?

Answer: For arbitrary numbers 747, 542 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.