Highest Common Factor of 477, 777, 106 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 477, 777, 106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 477, 777, 106 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 477, 777, 106 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 477, 777, 106 is 1.

HCF(477, 777, 106) = 1

HCF of 477, 777, 106 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 477, 777, 106 is 1.

Highest Common Factor of 477,777,106 using Euclid's algorithm

Highest Common Factor of 477,777,106 is 1

Step 1: Since 777 > 477, we apply the division lemma to 777 and 477, to get

777 = 477 x 1 + 300

Step 2: Since the reminder 477 ≠ 0, we apply division lemma to 300 and 477, to get

477 = 300 x 1 + 177

Step 3: We consider the new divisor 300 and the new remainder 177, and apply the division lemma to get

300 = 177 x 1 + 123

We consider the new divisor 177 and the new remainder 123,and apply the division lemma to get

177 = 123 x 1 + 54

We consider the new divisor 123 and the new remainder 54,and apply the division lemma to get

123 = 54 x 2 + 15

We consider the new divisor 54 and the new remainder 15,and apply the division lemma to get

54 = 15 x 3 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 477 and 777 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(123,54) = HCF(177,123) = HCF(300,177) = HCF(477,300) = HCF(777,477) .

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

Step 1: Since 106 > 3, we apply the division lemma to 106 and 3, to get

106 = 3 x 35 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 106 is 1

Notice that 1 = HCF(3,1) = HCF(106,3) .

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Frequently Asked Questions on HCF of 477, 777, 106 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 477, 777, 106?

Answer: HCF of 477, 777, 106 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 477, 777, 106 using Euclid's Algorithm?

Answer: For arbitrary numbers 477, 777, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.