Highest Common Factor of 2277, 9285, 70574 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 2277, 9285, 70574 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2277, 9285, 70574 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 2277, 9285, 70574 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 2277, 9285, 70574 is 1.

HCF(2277, 9285, 70574) = 1

HCF of 2277, 9285, 70574 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 2277, 9285, 70574 is 1.

Highest Common Factor of 2277,9285,70574 using Euclid's algorithm

Highest Common Factor of 2277,9285,70574 is 1

Step 1: Since 9285 > 2277, we apply the division lemma to 9285 and 2277, to get

9285 = 2277 x 4 + 177

Step 2: Since the reminder 2277 ≠ 0, we apply division lemma to 177 and 2277, to get

2277 = 177 x 12 + 153

Step 3: We consider the new divisor 177 and the new remainder 153, and apply the division lemma to get

177 = 153 x 1 + 24

We consider the new divisor 153 and the new remainder 24,and apply the division lemma to get

153 = 24 x 6 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 6

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 2277 and 9285 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(153,24) = HCF(177,153) = HCF(2277,177) = HCF(9285,2277) .

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

Step 1: Since 70574 > 3, we apply the division lemma to 70574 and 3, to get

70574 = 3 x 23524 + 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 70574 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(70574,3) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 2277, 9285, 70574 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 2277, 9285, 70574?

Answer: HCF of 2277, 9285, 70574 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2277, 9285, 70574 using Euclid's Algorithm?

Answer: For arbitrary numbers 2277, 9285, 70574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.