Highest Common Factor of 721, 4007 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 721, 4007 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 721, 4007 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 721, 4007 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 721, 4007 is 1.

HCF(721, 4007) = 1

HCF of 721, 4007 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 721, 4007 is 1.

Highest Common Factor of 721,4007 using Euclid's algorithm

Highest Common Factor of 721,4007 is 1

Step 1: Since 4007 > 721, we apply the division lemma to 4007 and 721, to get

4007 = 721 x 5 + 402

Step 2: Since the reminder 721 ≠ 0, we apply division lemma to 402 and 721, to get

721 = 402 x 1 + 319

Step 3: We consider the new divisor 402 and the new remainder 319, and apply the division lemma to get

402 = 319 x 1 + 83

We consider the new divisor 319 and the new remainder 83,and apply the division lemma to get

319 = 83 x 3 + 70

We consider the new divisor 83 and the new remainder 70,and apply the division lemma to get

83 = 70 x 1 + 13

We consider the new divisor 70 and the new remainder 13,and apply the division lemma to get

70 = 13 x 5 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 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 721 and 4007 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(70,13) = HCF(83,70) = HCF(319,83) = HCF(402,319) = HCF(721,402) = HCF(4007,721) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 721, 4007 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 721, 4007?

Answer: HCF of 721, 4007 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 721, 4007 using Euclid's Algorithm?

Answer: For arbitrary numbers 721, 4007 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.