Highest Common Factor of 450, 255, 54 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 450, 255, 54 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 450, 255, 54 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 450, 255, 54 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 450, 255, 54 is 3.

HCF(450, 255, 54) = 3

HCF of 450, 255, 54 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 450, 255, 54 is 3.

Highest Common Factor of 450,255,54 using Euclid's algorithm

Highest Common Factor of 450,255,54 is 3

Step 1: Since 450 > 255, we apply the division lemma to 450 and 255, to get

450 = 255 x 1 + 195

Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 195 and 255, to get

255 = 195 x 1 + 60

Step 3: We consider the new divisor 195 and the new remainder 60, and apply the division lemma to get

195 = 60 x 3 + 15

We consider the new divisor 60 and the new remainder 15, and apply the division lemma to get

60 = 15 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 450 and 255 is 15

Notice that 15 = HCF(60,15) = HCF(195,60) = HCF(255,195) = HCF(450,255) .

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

Step 1: Since 54 > 15, we apply the division lemma to 54 and 15, to get

54 = 15 x 3 + 9

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 9 and 15, to get

15 = 9 x 1 + 6

Step 3: 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 15 and 54 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) .

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Frequently Asked Questions on HCF of 450, 255, 54 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 450, 255, 54?

Answer: HCF of 450, 255, 54 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 450, 255, 54 using Euclid's Algorithm?

Answer: For arbitrary numbers 450, 255, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.