Highest Common Factor of 5802, 8210 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 5802, 8210 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 5802, 8210 is 2 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 5802, 8210 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 5802, 8210 is 2.

HCF(5802, 8210) = 2

HCF of 5802, 8210 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 5802, 8210 is 2.

Highest Common Factor of 5802,8210 using Euclid's algorithm

Highest Common Factor of 5802,8210 is 2

Step 1: Since 8210 > 5802, we apply the division lemma to 8210 and 5802, to get

8210 = 5802 x 1 + 2408

Step 2: Since the reminder 5802 ≠ 0, we apply division lemma to 2408 and 5802, to get

5802 = 2408 x 2 + 986

Step 3: We consider the new divisor 2408 and the new remainder 986, and apply the division lemma to get

2408 = 986 x 2 + 436

We consider the new divisor 986 and the new remainder 436,and apply the division lemma to get

986 = 436 x 2 + 114

We consider the new divisor 436 and the new remainder 114,and apply the division lemma to get

436 = 114 x 3 + 94

We consider the new divisor 114 and the new remainder 94,and apply the division lemma to get

114 = 94 x 1 + 20

We consider the new divisor 94 and the new remainder 20,and apply the division lemma to get

94 = 20 x 4 + 14

We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get

20 = 14 x 1 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5802 and 8210 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(94,20) = HCF(114,94) = HCF(436,114) = HCF(986,436) = HCF(2408,986) = HCF(5802,2408) = HCF(8210,5802) .

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Frequently Asked Questions on HCF of 5802, 8210 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 5802, 8210?

Answer: HCF of 5802, 8210 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5802, 8210 using Euclid's Algorithm?

Answer: For arbitrary numbers 5802, 8210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.