Highest Common Factor of 8228, 7005 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 8228, 7005 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8228, 7005 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 8228, 7005 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 8228, 7005 is 1.

HCF(8228, 7005) = 1

HCF of 8228, 7005 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 8228, 7005 is 1.

Highest Common Factor of 8228,7005 using Euclid's algorithm

Highest Common Factor of 8228,7005 is 1

Step 1: Since 8228 > 7005, we apply the division lemma to 8228 and 7005, to get

8228 = 7005 x 1 + 1223

Step 2: Since the reminder 7005 ≠ 0, we apply division lemma to 1223 and 7005, to get

7005 = 1223 x 5 + 890

Step 3: We consider the new divisor 1223 and the new remainder 890, and apply the division lemma to get

1223 = 890 x 1 + 333

We consider the new divisor 890 and the new remainder 333,and apply the division lemma to get

890 = 333 x 2 + 224

We consider the new divisor 333 and the new remainder 224,and apply the division lemma to get

333 = 224 x 1 + 109

We consider the new divisor 224 and the new remainder 109,and apply the division lemma to get

224 = 109 x 2 + 6

We consider the new divisor 109 and the new remainder 6,and apply the division lemma to get

109 = 6 x 18 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma 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 8228 and 7005 is 1

Notice that 1 = HCF(6,1) = HCF(109,6) = HCF(224,109) = HCF(333,224) = HCF(890,333) = HCF(1223,890) = HCF(7005,1223) = HCF(8228,7005) .

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Frequently Asked Questions on HCF of 8228, 7005 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 8228, 7005?

Answer: HCF of 8228, 7005 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8228, 7005 using Euclid's Algorithm?

Answer: For arbitrary numbers 8228, 7005 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.