Highest Common Factor of 704, 8229, 2016 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 704, 8229, 2016 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 704, 8229, 2016 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 704, 8229, 2016 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 704, 8229, 2016 is 1.

HCF(704, 8229, 2016) = 1

HCF of 704, 8229, 2016 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 704, 8229, 2016 is 1.

Highest Common Factor of 704,8229,2016 using Euclid's algorithm

Highest Common Factor of 704,8229,2016 is 1

Step 1: Since 8229 > 704, we apply the division lemma to 8229 and 704, to get

8229 = 704 x 11 + 485

Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 485 and 704, to get

704 = 485 x 1 + 219

Step 3: We consider the new divisor 485 and the new remainder 219, and apply the division lemma to get

485 = 219 x 2 + 47

We consider the new divisor 219 and the new remainder 47,and apply the division lemma to get

219 = 47 x 4 + 31

We consider the new divisor 47 and the new remainder 31,and apply the division lemma to get

47 = 31 x 1 + 16

We consider the new divisor 31 and the new remainder 16,and apply the division lemma to get

31 = 16 x 1 + 15

We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get

16 = 15 x 1 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 704 and 8229 is 1

Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(31,16) = HCF(47,31) = HCF(219,47) = HCF(485,219) = HCF(704,485) = HCF(8229,704) .

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

Step 1: Since 2016 > 1, we apply the division lemma to 2016 and 1, to get

2016 = 1 x 2016 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2016 is 1

Notice that 1 = HCF(2016,1) .

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Frequently Asked Questions on HCF of 704, 8229, 2016 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 704, 8229, 2016?

Answer: HCF of 704, 8229, 2016 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 704, 8229, 2016 using Euclid's Algorithm?

Answer: For arbitrary numbers 704, 8229, 2016 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.