Highest Common Factor of 713, 441, 345 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 713, 441, 345 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 713, 441, 345 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 713, 441, 345 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 713, 441, 345 is 1.

HCF(713, 441, 345) = 1

HCF of 713, 441, 345 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 713, 441, 345 is 1.

Highest Common Factor of 713,441,345 using Euclid's algorithm

Highest Common Factor of 713,441,345 is 1

Step 1: Since 713 > 441, we apply the division lemma to 713 and 441, to get

713 = 441 x 1 + 272

Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 272 and 441, to get

441 = 272 x 1 + 169

Step 3: We consider the new divisor 272 and the new remainder 169, and apply the division lemma to get

272 = 169 x 1 + 103

We consider the new divisor 169 and the new remainder 103,and apply the division lemma to get

169 = 103 x 1 + 66

We consider the new divisor 103 and the new remainder 66,and apply the division lemma to get

103 = 66 x 1 + 37

We consider the new divisor 66 and the new remainder 37,and apply the division lemma to get

66 = 37 x 1 + 29

We consider the new divisor 37 and the new remainder 29,and apply the division lemma to get

37 = 29 x 1 + 8

We consider the new divisor 29 and the new remainder 8,and apply the division lemma to get

29 = 8 x 3 + 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 713 and 441 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(37,29) = HCF(66,37) = HCF(103,66) = HCF(169,103) = HCF(272,169) = HCF(441,272) = HCF(713,441) .

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

Step 1: Since 345 > 1, we apply the division lemma to 345 and 1, to get

345 = 1 x 345 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 345 is 1

Notice that 1 = HCF(345,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 713, 441, 345 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 713, 441, 345?

Answer: HCF of 713, 441, 345 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 713, 441, 345 using Euclid's Algorithm?

Answer: For arbitrary numbers 713, 441, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.