Highest Common Factor of 663, 468, 990 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, 468, 990 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 663, 468, 990 is 3 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, 468, 990 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, 468, 990 is 3.

HCF(663, 468, 990) = 3

HCF of 663, 468, 990 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, 468, 990 is 3.

Highest Common Factor of 663,468,990 using Euclid's algorithm

Highest Common Factor of 663,468,990 is 3

Step 1: Since 663 > 468, we apply the division lemma to 663 and 468, to get

663 = 468 x 1 + 195

Step 2: Since the reminder 468 ≠ 0, we apply division lemma to 195 and 468, to get

468 = 195 x 2 + 78

Step 3: We consider the new divisor 195 and the new remainder 78, and apply the division lemma to get

195 = 78 x 2 + 39

We consider the new divisor 78 and the new remainder 39, and apply the division lemma to get

78 = 39 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 663 and 468 is 39

Notice that 39 = HCF(78,39) = HCF(195,78) = HCF(468,195) = HCF(663,468) .

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

Step 1: Since 990 > 39, we apply the division lemma to 990 and 39, to get

990 = 39 x 25 + 15

Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 15 and 39, to get

39 = 15 x 2 + 9

Step 3: We consider the new divisor 15 and the new remainder 9, and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 39 and 990 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(990,39) .

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Frequently Asked Questions on HCF of 663, 468, 990 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, 468, 990?

Answer: HCF of 663, 468, 990 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 663, 468, 990 using Euclid's Algorithm?

Answer: For arbitrary numbers 663, 468, 990 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.