Highest Common Factor of 106, 486, 477 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 106, 486, 477 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 106, 486, 477 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 106, 486, 477 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 106, 486, 477 is 1.

HCF(106, 486, 477) = 1

HCF of 106, 486, 477 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 106, 486, 477 is 1.

Highest Common Factor of 106,486,477 using Euclid's algorithm

Highest Common Factor of 106,486,477 is 1

Step 1: Since 486 > 106, we apply the division lemma to 486 and 106, to get

486 = 106 x 4 + 62

Step 2: Since the reminder 106 ≠ 0, we apply division lemma to 62 and 106, to get

106 = 62 x 1 + 44

Step 3: We consider the new divisor 62 and the new remainder 44, and apply the division lemma to get

62 = 44 x 1 + 18

We consider the new divisor 44 and the new remainder 18,and apply the division lemma to get

44 = 18 x 2 + 8

We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get

18 = 8 x 2 + 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 106 and 486 is 2

Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(44,18) = HCF(62,44) = HCF(106,62) = HCF(486,106) .

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

Step 1: Since 477 > 2, we apply the division lemma to 477 and 2, to get

477 = 2 x 238 + 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 477 is 1

Notice that 1 = HCF(2,1) = HCF(477,2) .

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Frequently Asked Questions on HCF of 106, 486, 477 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 106, 486, 477?

Answer: HCF of 106, 486, 477 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 106, 486, 477 using Euclid's Algorithm?

Answer: For arbitrary numbers 106, 486, 477 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.