Highest Common Factor of 663, 460, 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, 460, 816 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 460, 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, 460, 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, 460, 816 is 1.

HCF(663, 460, 816) = 1

HCF of 663, 460, 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, 460, 816 is 1.

Highest Common Factor of 663,460,816 using Euclid's algorithm

Highest Common Factor of 663,460,816 is 1

Step 1: Since 663 > 460, we apply the division lemma to 663 and 460, to get

663 = 460 x 1 + 203

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 203 and 460, to get

460 = 203 x 2 + 54

Step 3: We consider the new divisor 203 and the new remainder 54, and apply the division lemma to get

203 = 54 x 3 + 41

We consider the new divisor 54 and the new remainder 41,and apply the division lemma to get

54 = 41 x 1 + 13

We consider the new divisor 41 and the new remainder 13,and apply the division lemma to get

41 = 13 x 3 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 663 and 460 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(41,13) = HCF(54,41) = HCF(203,54) = HCF(460,203) = HCF(663,460) .

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) .

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Frequently Asked Questions on HCF of 663, 460, 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, 460, 816?

Answer: HCF of 663, 460, 816 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 460, 816 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 460, 816 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.