Highest Common Factor of 896, 1697, 7114 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 896, 1697, 7114 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 896, 1697, 7114 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 896, 1697, 7114 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 896, 1697, 7114 is 1.

HCF(896, 1697, 7114) = 1

HCF of 896, 1697, 7114 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 896, 1697, 7114 is 1.

Highest Common Factor of 896,1697,7114 using Euclid's algorithm

Highest Common Factor of 896,1697,7114 is 1

Step 1: Since 1697 > 896, we apply the division lemma to 1697 and 896, to get

1697 = 896 x 1 + 801

Step 2: Since the reminder 896 ≠ 0, we apply division lemma to 801 and 896, to get

896 = 801 x 1 + 95

Step 3: We consider the new divisor 801 and the new remainder 95, and apply the division lemma to get

801 = 95 x 8 + 41

We consider the new divisor 95 and the new remainder 41,and apply the division lemma to get

95 = 41 x 2 + 13

We consider the new divisor 41 and the new remainder 13,and apply the division lemma to get

41 = 13 x 3 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 896 and 1697 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(41,13) = HCF(95,41) = HCF(801,95) = HCF(896,801) = HCF(1697,896) .

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

Step 1: Since 7114 > 1, we apply the division lemma to 7114 and 1, to get

7114 = 1 x 7114 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7114 is 1

Notice that 1 = HCF(7114,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 896, 1697, 7114 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 896, 1697, 7114?

Answer: HCF of 896, 1697, 7114 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 896, 1697, 7114 using Euclid's Algorithm?

Answer: For arbitrary numbers 896, 1697, 7114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.