Highest Common Factor of 462, 827, 696 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 462, 827, 696 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 462, 827, 696 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 462, 827, 696 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 462, 827, 696 is 1.

HCF(462, 827, 696) = 1

HCF of 462, 827, 696 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 462, 827, 696 is 1.

Highest Common Factor of 462,827,696 using Euclid's algorithm

Highest Common Factor of 462,827,696 is 1

Step 1: Since 827 > 462, we apply the division lemma to 827 and 462, to get

827 = 462 x 1 + 365

Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 365 and 462, to get

462 = 365 x 1 + 97

Step 3: We consider the new divisor 365 and the new remainder 97, and apply the division lemma to get

365 = 97 x 3 + 74

We consider the new divisor 97 and the new remainder 74,and apply the division lemma to get

97 = 74 x 1 + 23

We consider the new divisor 74 and the new remainder 23,and apply the division lemma to get

74 = 23 x 3 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

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 462 and 827 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(74,23) = HCF(97,74) = HCF(365,97) = HCF(462,365) = HCF(827,462) .

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

Step 1: Since 696 > 1, we apply the division lemma to 696 and 1, to get

696 = 1 x 696 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 696 is 1

Notice that 1 = HCF(696,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 462, 827, 696 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 462, 827, 696?

Answer: HCF of 462, 827, 696 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 462, 827, 696 using Euclid's Algorithm?

Answer: For arbitrary numbers 462, 827, 696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.