Highest Common Factor of 255, 448, 221 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 255, 448, 221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 255, 448, 221 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 255, 448, 221 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 255, 448, 221 is 1.

HCF(255, 448, 221) = 1

HCF of 255, 448, 221 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 255, 448, 221 is 1.

Highest Common Factor of 255,448,221 using Euclid's algorithm

Highest Common Factor of 255,448,221 is 1

Step 1: Since 448 > 255, we apply the division lemma to 448 and 255, to get

448 = 255 x 1 + 193

Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 193 and 255, to get

255 = 193 x 1 + 62

Step 3: We consider the new divisor 193 and the new remainder 62, and apply the division lemma to get

193 = 62 x 3 + 7

We consider the new divisor 62 and the new remainder 7,and apply the division lemma to get

62 = 7 x 8 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 255 and 448 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(62,7) = HCF(193,62) = HCF(255,193) = HCF(448,255) .

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

Step 1: Since 221 > 1, we apply the division lemma to 221 and 1, to get

221 = 1 x 221 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 221 is 1

Notice that 1 = HCF(221,1) .

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Frequently Asked Questions on HCF of 255, 448, 221 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 255, 448, 221?

Answer: HCF of 255, 448, 221 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 255, 448, 221 using Euclid's Algorithm?

Answer: For arbitrary numbers 255, 448, 221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.