Highest Common Factor of 480, 663, 441 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 480, 663, 441 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 480, 663, 441 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 480, 663, 441 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 480, 663, 441 is 3.

HCF(480, 663, 441) = 3

HCF of 480, 663, 441 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 480, 663, 441 is 3.

Highest Common Factor of 480,663,441 using Euclid's algorithm

Highest Common Factor of 480,663,441 is 3

Step 1: Since 663 > 480, we apply the division lemma to 663 and 480, to get

663 = 480 x 1 + 183

Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 183 and 480, to get

480 = 183 x 2 + 114

Step 3: We consider the new divisor 183 and the new remainder 114, and apply the division lemma to get

183 = 114 x 1 + 69

We consider the new divisor 114 and the new remainder 69,and apply the division lemma to get

114 = 69 x 1 + 45

We consider the new divisor 69 and the new remainder 45,and apply the division lemma to get

69 = 45 x 1 + 24

We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get

45 = 24 x 1 + 21

We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get

24 = 21 x 1 + 3

We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 480 and 663 is 3

Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(69,45) = HCF(114,69) = HCF(183,114) = HCF(480,183) = HCF(663,480) .

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

Step 1: Since 441 > 3, we apply the division lemma to 441 and 3, to get

441 = 3 x 147 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 441 is 3

Notice that 3 = HCF(441,3) .

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Frequently Asked Questions on HCF of 480, 663, 441 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 480, 663, 441?

Answer: HCF of 480, 663, 441 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 480, 663, 441 using Euclid's Algorithm?

Answer: For arbitrary numbers 480, 663, 441 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.