Highest Common Factor of 862, 682, 362 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 862, 682, 362 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 862, 682, 362 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 862, 682, 362 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 862, 682, 362 is 2.

HCF(862, 682, 362) = 2

HCF of 862, 682, 362 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 862, 682, 362 is 2.

Highest Common Factor of 862,682,362 using Euclid's algorithm

Highest Common Factor of 862,682,362 is 2

Step 1: Since 862 > 682, we apply the division lemma to 862 and 682, to get

862 = 682 x 1 + 180

Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 180 and 682, to get

682 = 180 x 3 + 142

Step 3: We consider the new divisor 180 and the new remainder 142, and apply the division lemma to get

180 = 142 x 1 + 38

We consider the new divisor 142 and the new remainder 38,and apply the division lemma to get

142 = 38 x 3 + 28

We consider the new divisor 38 and the new remainder 28,and apply the division lemma to get

38 = 28 x 1 + 10

We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get

28 = 10 x 2 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 862 and 682 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(142,38) = HCF(180,142) = HCF(682,180) = HCF(862,682) .

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

Step 1: Since 362 > 2, we apply the division lemma to 362 and 2, to get

362 = 2 x 181 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 362 is 2

Notice that 2 = HCF(362,2) .

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Frequently Asked Questions on HCF of 862, 682, 362 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 862, 682, 362?

Answer: HCF of 862, 682, 362 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 862, 682, 362 using Euclid's Algorithm?

Answer: For arbitrary numbers 862, 682, 362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.