Highest Common Factor of 663, 172, 816 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 663, 172, 816 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 172, 816 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 663, 172, 816 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 663, 172, 816 is 1.

HCF(663, 172, 816) = 1

HCF of 663, 172, 816 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 663, 172, 816 is 1.

Highest Common Factor of 663,172,816 using Euclid's algorithm

Highest Common Factor of 663,172,816 is 1

Step 1: Since 663 > 172, we apply the division lemma to 663 and 172, to get

663 = 172 x 3 + 147

Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 147 and 172, to get

172 = 147 x 1 + 25

Step 3: We consider the new divisor 147 and the new remainder 25, and apply the division lemma to get

147 = 25 x 5 + 22

We consider the new divisor 25 and the new remainder 22,and apply the division lemma to get

25 = 22 x 1 + 3

We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get

22 = 3 x 7 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 663 and 172 is 1

Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(25,22) = HCF(147,25) = HCF(172,147) = HCF(663,172) .

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

Step 1: Since 816 > 1, we apply the division lemma to 816 and 1, to get

816 = 1 x 816 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 816 is 1

Notice that 1 = HCF(816,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 663, 172, 816 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 663, 172, 816?

Answer: HCF of 663, 172, 816 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 172, 816 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 172, 816 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.