Highest Common Factor of 828, 219, 301 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 828, 219, 301 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 828, 219, 301 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 828, 219, 301 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 828, 219, 301 is 1.

HCF(828, 219, 301) = 1

HCF of 828, 219, 301 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 828, 219, 301 is 1.

Highest Common Factor of 828,219,301 using Euclid's algorithm

Highest Common Factor of 828,219,301 is 1

Step 1: Since 828 > 219, we apply the division lemma to 828 and 219, to get

828 = 219 x 3 + 171

Step 2: Since the reminder 219 ≠ 0, we apply division lemma to 171 and 219, to get

219 = 171 x 1 + 48

Step 3: We consider the new divisor 171 and the new remainder 48, and apply the division lemma to get

171 = 48 x 3 + 27

We consider the new divisor 48 and the new remainder 27,and apply the division lemma to get

48 = 27 x 1 + 21

We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get

27 = 21 x 1 + 6

We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get

21 = 6 x 3 + 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 828 and 219 is 3

Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(48,27) = HCF(171,48) = HCF(219,171) = HCF(828,219) .

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

Step 1: Since 301 > 3, we apply the division lemma to 301 and 3, to get

301 = 3 x 100 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 301 is 1

Notice that 1 = HCF(3,1) = HCF(301,3) .

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Frequently Asked Questions on HCF of 828, 219, 301 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 828, 219, 301?

Answer: HCF of 828, 219, 301 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 828, 219, 301 using Euclid's Algorithm?

Answer: For arbitrary numbers 828, 219, 301 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.