Highest Common Factor of 480, 660, 285 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, 660, 285 i.e. 15 the largest integer that leaves a remainder zero for all numbers.

HCF of 480, 660, 285 is 15 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, 660, 285 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, 660, 285 is 15.

HCF(480, 660, 285) = 15

HCF of 480, 660, 285 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, 660, 285 is 15.

Highest Common Factor of 480,660,285 using Euclid's algorithm

Highest Common Factor of 480,660,285 is 15

Step 1: Since 660 > 480, we apply the division lemma to 660 and 480, to get

660 = 480 x 1 + 180

Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 180 and 480, to get

480 = 180 x 2 + 120

Step 3: We consider the new divisor 180 and the new remainder 120, and apply the division lemma to get

180 = 120 x 1 + 60

We consider the new divisor 120 and the new remainder 60, and apply the division lemma to get

120 = 60 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 60, the HCF of 480 and 660 is 60

Notice that 60 = HCF(120,60) = HCF(180,120) = HCF(480,180) = HCF(660,480) .

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

Step 1: Since 285 > 60, we apply the division lemma to 285 and 60, to get

285 = 60 x 4 + 45

Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 45 and 60, to get

60 = 45 x 1 + 15

Step 3: We consider the new divisor 45 and the new remainder 15, and apply the division lemma to get

45 = 15 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 60 and 285 is 15

Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(285,60) .

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Frequently Asked Questions on HCF of 480, 660, 285 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, 660, 285?

Answer: HCF of 480, 660, 285 is 15 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 480, 660, 285 using Euclid's Algorithm?

Answer: For arbitrary numbers 480, 660, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.