Highest Common Factor of 605, 357, 560 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 605, 357, 560 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 605, 357, 560 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 605, 357, 560 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 605, 357, 560 is 1.

HCF(605, 357, 560) = 1

HCF of 605, 357, 560 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 605, 357, 560 is 1.

Highest Common Factor of 605,357,560 using Euclid's algorithm

Highest Common Factor of 605,357,560 is 1

Step 1: Since 605 > 357, we apply the division lemma to 605 and 357, to get

605 = 357 x 1 + 248

Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 248 and 357, to get

357 = 248 x 1 + 109

Step 3: We consider the new divisor 248 and the new remainder 109, and apply the division lemma to get

248 = 109 x 2 + 30

We consider the new divisor 109 and the new remainder 30,and apply the division lemma to get

109 = 30 x 3 + 19

We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get

30 = 19 x 1 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 605 and 357 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(109,30) = HCF(248,109) = HCF(357,248) = HCF(605,357) .

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

Step 1: Since 560 > 1, we apply the division lemma to 560 and 1, to get

560 = 1 x 560 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 560 is 1

Notice that 1 = HCF(560,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 605, 357, 560 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 605, 357, 560?

Answer: HCF of 605, 357, 560 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 605, 357, 560 using Euclid's Algorithm?

Answer: For arbitrary numbers 605, 357, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.