Highest Common Factor of 704, 269, 763 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 704, 269, 763 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 704, 269, 763 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 704, 269, 763 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 704, 269, 763 is 1.

HCF(704, 269, 763) = 1

HCF of 704, 269, 763 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 704, 269, 763 is 1.

Highest Common Factor of 704,269,763 using Euclid's algorithm

Highest Common Factor of 704,269,763 is 1

Step 1: Since 704 > 269, we apply the division lemma to 704 and 269, to get

704 = 269 x 2 + 166

Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 166 and 269, to get

269 = 166 x 1 + 103

Step 3: We consider the new divisor 166 and the new remainder 103, and apply the division lemma to get

166 = 103 x 1 + 63

We consider the new divisor 103 and the new remainder 63,and apply the division lemma to get

103 = 63 x 1 + 40

We consider the new divisor 63 and the new remainder 40,and apply the division lemma to get

63 = 40 x 1 + 23

We consider the new divisor 40 and the new remainder 23,and apply the division lemma to get

40 = 23 x 1 + 17

We consider the new divisor 23 and the new remainder 17,and apply the division lemma to get

23 = 17 x 1 + 6

We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get

17 = 6 x 2 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 704 and 269 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(23,17) = HCF(40,23) = HCF(63,40) = HCF(103,63) = HCF(166,103) = HCF(269,166) = HCF(704,269) .

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

Step 1: Since 763 > 1, we apply the division lemma to 763 and 1, to get

763 = 1 x 763 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 763 is 1

Notice that 1 = HCF(763,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 704, 269, 763 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 704, 269, 763?

Answer: HCF of 704, 269, 763 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 704, 269, 763 using Euclid's Algorithm?

Answer: For arbitrary numbers 704, 269, 763 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.