Highest Common Factor of 182, 466, 298 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 182, 466, 298 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 182, 466, 298 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 182, 466, 298 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 182, 466, 298 is 2.

HCF(182, 466, 298) = 2

HCF of 182, 466, 298 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 182, 466, 298 is 2.

Highest Common Factor of 182,466,298 using Euclid's algorithm

Highest Common Factor of 182,466,298 is 2

Step 1: Since 466 > 182, we apply the division lemma to 466 and 182, to get

466 = 182 x 2 + 102

Step 2: Since the reminder 182 ≠ 0, we apply division lemma to 102 and 182, to get

182 = 102 x 1 + 80

Step 3: We consider the new divisor 102 and the new remainder 80, and apply the division lemma to get

102 = 80 x 1 + 22

We consider the new divisor 80 and the new remainder 22,and apply the division lemma to get

80 = 22 x 3 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 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 182 and 466 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(80,22) = HCF(102,80) = HCF(182,102) = HCF(466,182) .

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

Step 1: Since 298 > 2, we apply the division lemma to 298 and 2, to get

298 = 2 x 149 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 298 is 2

Notice that 2 = HCF(298,2) .

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Frequently Asked Questions on HCF of 182, 466, 298 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 182, 466, 298?

Answer: HCF of 182, 466, 298 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 182, 466, 298 using Euclid's Algorithm?

Answer: For arbitrary numbers 182, 466, 298 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.