Highest Common Factor of 146, 2108, 6327 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 146, 2108, 6327 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 146, 2108, 6327 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 146, 2108, 6327 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 146, 2108, 6327 is 1.

HCF(146, 2108, 6327) = 1

HCF of 146, 2108, 6327 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 146, 2108, 6327 is 1.

Highest Common Factor of 146,2108,6327 using Euclid's algorithm

Highest Common Factor of 146,2108,6327 is 1

Step 1: Since 2108 > 146, we apply the division lemma to 2108 and 146, to get

2108 = 146 x 14 + 64

Step 2: Since the reminder 146 ≠ 0, we apply division lemma to 64 and 146, to get

146 = 64 x 2 + 18

Step 3: We consider the new divisor 64 and the new remainder 18, and apply the division lemma to get

64 = 18 x 3 + 10

We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get

18 = 10 x 1 + 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 146 and 2108 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(64,18) = HCF(146,64) = HCF(2108,146) .

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

Step 1: Since 6327 > 2, we apply the division lemma to 6327 and 2, to get

6327 = 2 x 3163 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 6327 is 1

Notice that 1 = HCF(2,1) = HCF(6327,2) .

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Frequently Asked Questions on HCF of 146, 2108, 6327 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 146, 2108, 6327?

Answer: HCF of 146, 2108, 6327 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 146, 2108, 6327 using Euclid's Algorithm?

Answer: For arbitrary numbers 146, 2108, 6327 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.