Highest Common Factor of 487, 756 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 487, 756 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 487, 756 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 487, 756 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 487, 756 is 1.

HCF(487, 756) = 1

HCF of 487, 756 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 487, 756 is 1.

Highest Common Factor of 487,756 using Euclid's algorithm

Highest Common Factor of 487,756 is 1

Step 1: Since 756 > 487, we apply the division lemma to 756 and 487, to get

756 = 487 x 1 + 269

Step 2: Since the reminder 487 ≠ 0, we apply division lemma to 269 and 487, to get

487 = 269 x 1 + 218

Step 3: We consider the new divisor 269 and the new remainder 218, and apply the division lemma to get

269 = 218 x 1 + 51

We consider the new divisor 218 and the new remainder 51,and apply the division lemma to get

218 = 51 x 4 + 14

We consider the new divisor 51 and the new remainder 14,and apply the division lemma to get

51 = 14 x 3 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 487 and 756 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(51,14) = HCF(218,51) = HCF(269,218) = HCF(487,269) = HCF(756,487) .

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Frequently Asked Questions on HCF of 487, 756 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 487, 756?

Answer: HCF of 487, 756 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 487, 756 using Euclid's Algorithm?

Answer: For arbitrary numbers 487, 756 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.