Highest Common Factor of 984, 697, 14 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 984, 697, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 984, 697, 14 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 984, 697, 14 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 984, 697, 14 is 1.

HCF(984, 697, 14) = 1

HCF of 984, 697, 14 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 984, 697, 14 is 1.

Highest Common Factor of 984,697,14 using Euclid's algorithm

Highest Common Factor of 984,697,14 is 1

Step 1: Since 984 > 697, we apply the division lemma to 984 and 697, to get

984 = 697 x 1 + 287

Step 2: Since the reminder 697 ≠ 0, we apply division lemma to 287 and 697, to get

697 = 287 x 2 + 123

Step 3: We consider the new divisor 287 and the new remainder 123, and apply the division lemma to get

287 = 123 x 2 + 41

We consider the new divisor 123 and the new remainder 41, and apply the division lemma to get

123 = 41 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 41, the HCF of 984 and 697 is 41

Notice that 41 = HCF(123,41) = HCF(287,123) = HCF(697,287) = HCF(984,697) .

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

Step 1: Since 41 > 14, we apply the division lemma to 41 and 14, to get

41 = 14 x 2 + 13

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 13 and 14, to get

14 = 13 x 1 + 1

Step 3: We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 41 and 14 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(41,14) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 984, 697, 14 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 984, 697, 14?

Answer: HCF of 984, 697, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 984, 697, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 984, 697, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.