Highest Common Factor of 714, 697 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 714, 697 i.e. 17 the largest integer that leaves a remainder zero for all numbers.

HCF of 714, 697 is 17 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 714, 697 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 714, 697 is 17.

HCF(714, 697) = 17

HCF of 714, 697 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 714, 697 is 17.

Highest Common Factor of 714,697 using Euclid's algorithm

Highest Common Factor of 714,697 is 17

Step 1: Since 714 > 697, we apply the division lemma to 714 and 697, to get

714 = 697 x 1 + 17

Step 2: Since the reminder 697 ≠ 0, we apply division lemma to 17 and 697, to get

697 = 17 x 41 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 714 and 697 is 17

Notice that 17 = HCF(697,17) = HCF(714,697) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 714, 697 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 714, 697?

Answer: HCF of 714, 697 is 17 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 714, 697 using Euclid's Algorithm?

Answer: For arbitrary numbers 714, 697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.