Highest Common Factor of 3999, 721 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 3999, 721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3999, 721 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 3999, 721 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 3999, 721 is 1.

HCF(3999, 721) = 1

HCF of 3999, 721 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 3999, 721 is 1.

Highest Common Factor of 3999,721 using Euclid's algorithm

Highest Common Factor of 3999,721 is 1

Step 1: Since 3999 > 721, we apply the division lemma to 3999 and 721, to get

3999 = 721 x 5 + 394

Step 2: Since the reminder 721 ≠ 0, we apply division lemma to 394 and 721, to get

721 = 394 x 1 + 327

Step 3: We consider the new divisor 394 and the new remainder 327, and apply the division lemma to get

394 = 327 x 1 + 67

We consider the new divisor 327 and the new remainder 67,and apply the division lemma to get

327 = 67 x 4 + 59

We consider the new divisor 67 and the new remainder 59,and apply the division lemma to get

67 = 59 x 1 + 8

We consider the new divisor 59 and the new remainder 8,and apply the division lemma to get

59 = 8 x 7 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 3999 and 721 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(59,8) = HCF(67,59) = HCF(327,67) = HCF(394,327) = HCF(721,394) = HCF(3999,721) .

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Frequently Asked Questions on HCF of 3999, 721 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 3999, 721?

Answer: HCF of 3999, 721 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3999, 721 using Euclid's Algorithm?

Answer: For arbitrary numbers 3999, 721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.