Highest Common Factor of 477, 699, 407 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, 699, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 477, 699, 407 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, 699, 407 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, 699, 407 is 1.

HCF(477, 699, 407) = 1

HCF of 477, 699, 407 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, 699, 407 is 1.

Highest Common Factor of 477,699,407 using Euclid's algorithm

Highest Common Factor of 477,699,407 is 1

Step 1: Since 699 > 477, we apply the division lemma to 699 and 477, to get

699 = 477 x 1 + 222

Step 2: Since the reminder 477 ≠ 0, we apply division lemma to 222 and 477, to get

477 = 222 x 2 + 33

Step 3: We consider the new divisor 222 and the new remainder 33, and apply the division lemma to get

222 = 33 x 6 + 24

We consider the new divisor 33 and the new remainder 24,and apply the division lemma to get

33 = 24 x 1 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 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 699 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(222,33) = HCF(477,222) = HCF(699,477) .

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

Step 1: Since 407 > 3, we apply the division lemma to 407 and 3, to get

407 = 3 x 135 + 2

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

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 407 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(407,3) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 477, 699, 407 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, 699, 407?

Answer: HCF of 477, 699, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 477, 699, 407 using Euclid's Algorithm?

Answer: For arbitrary numbers 477, 699, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.