Highest Common Factor of 691, 986, 304 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 691, 986, 304 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 986, 304 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 691, 986, 304 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 691, 986, 304 is 1.

HCF(691, 986, 304) = 1

HCF of 691, 986, 304 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 691, 986, 304 is 1.

Highest Common Factor of 691,986,304 using Euclid's algorithm

Highest Common Factor of 691,986,304 is 1

Step 1: Since 986 > 691, we apply the division lemma to 986 and 691, to get

986 = 691 x 1 + 295

Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 295 and 691, to get

691 = 295 x 2 + 101

Step 3: We consider the new divisor 295 and the new remainder 101, and apply the division lemma to get

295 = 101 x 2 + 93

We consider the new divisor 101 and the new remainder 93,and apply the division lemma to get

101 = 93 x 1 + 8

We consider the new divisor 93 and the new remainder 8,and apply the division lemma to get

93 = 8 x 11 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 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 691 and 986 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(93,8) = HCF(101,93) = HCF(295,101) = HCF(691,295) = HCF(986,691) .

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

Step 1: Since 304 > 1, we apply the division lemma to 304 and 1, to get

304 = 1 x 304 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 304 is 1

Notice that 1 = HCF(304,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 691, 986, 304 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 691, 986, 304?

Answer: HCF of 691, 986, 304 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 986, 304 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 986, 304 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.