Highest Common Factor of 747, 462, 521 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, 462, 521 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 747, 462, 521 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, 462, 521 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, 462, 521 is 1.

HCF(747, 462, 521) = 1

HCF of 747, 462, 521 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, 462, 521 is 1.

Highest Common Factor of 747,462,521 using Euclid's algorithm

Highest Common Factor of 747,462,521 is 1

Step 1: Since 747 > 462, we apply the division lemma to 747 and 462, to get

747 = 462 x 1 + 285

Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 285 and 462, to get

462 = 285 x 1 + 177

Step 3: We consider the new divisor 285 and the new remainder 177, and apply the division lemma to get

285 = 177 x 1 + 108

We consider the new divisor 177 and the new remainder 108,and apply the division lemma to get

177 = 108 x 1 + 69

We consider the new divisor 108 and the new remainder 69,and apply the division lemma to get

108 = 69 x 1 + 39

We consider the new divisor 69 and the new remainder 39,and apply the division lemma to get

69 = 39 x 1 + 30

We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get

39 = 30 x 1 + 9

We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get

30 = 9 x 3 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 747 and 462 is 3

Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(69,39) = HCF(108,69) = HCF(177,108) = HCF(285,177) = HCF(462,285) = HCF(747,462) .

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

Step 1: Since 521 > 3, we apply the division lemma to 521 and 3, to get

521 = 3 x 173 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 521 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(521,3) .

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Frequently Asked Questions on HCF of 747, 462, 521 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, 462, 521?

Answer: HCF of 747, 462, 521 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 747, 462, 521 using Euclid's Algorithm?

Answer: For arbitrary numbers 747, 462, 521 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.