Highest Common Factor of 882, 228, 721 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 882, 228, 721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 882, 228, 721 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 882, 228, 721 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 882, 228, 721 is 1.

HCF(882, 228, 721) = 1

HCF of 882, 228, 721 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 882, 228, 721 is 1.

Highest Common Factor of 882,228,721 using Euclid's algorithm

Highest Common Factor of 882,228,721 is 1

Step 1: Since 882 > 228, we apply the division lemma to 882 and 228, to get

882 = 228 x 3 + 198

Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 198 and 228, to get

228 = 198 x 1 + 30

Step 3: We consider the new divisor 198 and the new remainder 30, and apply the division lemma to get

198 = 30 x 6 + 18

We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get

30 = 18 x 1 + 12

We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get

18 = 12 x 1 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 882 and 228 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(198,30) = HCF(228,198) = HCF(882,228) .

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

Step 1: Since 721 > 6, we apply the division lemma to 721 and 6, to get

721 = 6 x 120 + 1

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, 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 6 and 721 is 1

Notice that 1 = HCF(6,1) = HCF(721,6) .

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Frequently Asked Questions on HCF of 882, 228, 721 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 882, 228, 721?

Answer: HCF of 882, 228, 721 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 882, 228, 721 using Euclid's Algorithm?

Answer: For arbitrary numbers 882, 228, 721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.