Highest Common Factor of 255, 7044, 6977 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, 7044, 6977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 255, 7044, 6977 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, 7044, 6977 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, 7044, 6977 is 1.

HCF(255, 7044, 6977) = 1

HCF of 255, 7044, 6977 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, 7044, 6977 is 1.

Highest Common Factor of 255,7044,6977 using Euclid's algorithm

Highest Common Factor of 255,7044,6977 is 1

Step 1: Since 7044 > 255, we apply the division lemma to 7044 and 255, to get

7044 = 255 x 27 + 159

Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 159 and 255, to get

255 = 159 x 1 + 96

Step 3: We consider the new divisor 159 and the new remainder 96, and apply the division lemma to get

159 = 96 x 1 + 63

We consider the new divisor 96 and the new remainder 63,and apply the division lemma to get

96 = 63 x 1 + 33

We consider the new divisor 63 and the new remainder 33,and apply the division lemma to get

63 = 33 x 1 + 30

We consider the new divisor 33 and the new remainder 30,and apply the division lemma to get

33 = 30 x 1 + 3

We consider the new divisor 30 and the new remainder 3,and apply the division lemma to get

30 = 3 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 255 and 7044 is 3

Notice that 3 = HCF(30,3) = HCF(33,30) = HCF(63,33) = HCF(96,63) = HCF(159,96) = HCF(255,159) = HCF(7044,255) .

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

Step 1: Since 6977 > 3, we apply the division lemma to 6977 and 3, to get

6977 = 3 x 2325 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 6977 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(6977,3) .

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Frequently Asked Questions on HCF of 255, 7044, 6977 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, 7044, 6977?

Answer: HCF of 255, 7044, 6977 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 255, 7044, 6977 using Euclid's Algorithm?

Answer: For arbitrary numbers 255, 7044, 6977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.