Highest Common Factor of 612, 827, 228 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 612, 827, 228 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 612, 827, 228 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 612, 827, 228 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 612, 827, 228 is 1.

HCF(612, 827, 228) = 1

HCF of 612, 827, 228 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 612, 827, 228 is 1.

Highest Common Factor of 612,827,228 using Euclid's algorithm

Highest Common Factor of 612,827,228 is 1

Step 1: Since 827 > 612, we apply the division lemma to 827 and 612, to get

827 = 612 x 1 + 215

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 215 and 612, to get

612 = 215 x 2 + 182

Step 3: We consider the new divisor 215 and the new remainder 182, and apply the division lemma to get

215 = 182 x 1 + 33

We consider the new divisor 182 and the new remainder 33,and apply the division lemma to get

182 = 33 x 5 + 17

We consider the new divisor 33 and the new remainder 17,and apply the division lemma to get

33 = 17 x 1 + 16

We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get

17 = 16 x 1 + 1

We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get

16 = 1 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 612 and 827 is 1

Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(33,17) = HCF(182,33) = HCF(215,182) = HCF(612,215) = HCF(827,612) .

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

Step 1: Since 228 > 1, we apply the division lemma to 228 and 1, to get

228 = 1 x 228 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 228 is 1

Notice that 1 = HCF(228,1) .

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Frequently Asked Questions on HCF of 612, 827, 228 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 612, 827, 228?

Answer: HCF of 612, 827, 228 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 612, 827, 228 using Euclid's Algorithm?

Answer: For arbitrary numbers 612, 827, 228 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.