Highest Common Factor of 721, 447, 999 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, 447, 999 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 721, 447, 999 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, 447, 999 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, 447, 999 is 1.

HCF(721, 447, 999) = 1

HCF of 721, 447, 999 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, 447, 999 is 1.

Highest Common Factor of 721,447,999 using Euclid's algorithm

Highest Common Factor of 721,447,999 is 1

Step 1: Since 721 > 447, we apply the division lemma to 721 and 447, to get

721 = 447 x 1 + 274

Step 2: Since the reminder 447 ≠ 0, we apply division lemma to 274 and 447, to get

447 = 274 x 1 + 173

Step 3: We consider the new divisor 274 and the new remainder 173, and apply the division lemma to get

274 = 173 x 1 + 101

We consider the new divisor 173 and the new remainder 101,and apply the division lemma to get

173 = 101 x 1 + 72

We consider the new divisor 101 and the new remainder 72,and apply the division lemma to get

101 = 72 x 1 + 29

We consider the new divisor 72 and the new remainder 29,and apply the division lemma to get

72 = 29 x 2 + 14

We consider the new divisor 29 and the new remainder 14,and apply the division lemma to get

29 = 14 x 2 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 721 and 447 is 1

Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(72,29) = HCF(101,72) = HCF(173,101) = HCF(274,173) = HCF(447,274) = HCF(721,447) .

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

Step 1: Since 999 > 1, we apply the division lemma to 999 and 1, to get

999 = 1 x 999 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 999 is 1

Notice that 1 = HCF(999,1) .

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Frequently Asked Questions on HCF of 721, 447, 999 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, 447, 999?

Answer: HCF of 721, 447, 999 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 721, 447, 999 using Euclid's Algorithm?

Answer: For arbitrary numbers 721, 447, 999 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.