Highest Common Factor of 296, 360, 645 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 296, 360, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 296, 360, 645 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 296, 360, 645 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 296, 360, 645 is 1.

HCF(296, 360, 645) = 1

HCF of 296, 360, 645 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 296, 360, 645 is 1.

Highest Common Factor of 296,360,645 using Euclid's algorithm

Highest Common Factor of 296,360,645 is 1

Step 1: Since 360 > 296, we apply the division lemma to 360 and 296, to get

360 = 296 x 1 + 64

Step 2: Since the reminder 296 ≠ 0, we apply division lemma to 64 and 296, to get

296 = 64 x 4 + 40

Step 3: We consider the new divisor 64 and the new remainder 40, and apply the division lemma to get

64 = 40 x 1 + 24

We consider the new divisor 40 and the new remainder 24,and apply the division lemma to get

40 = 24 x 1 + 16

We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get

24 = 16 x 1 + 8

We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 296 and 360 is 8

Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(40,24) = HCF(64,40) = HCF(296,64) = HCF(360,296) .

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

Step 1: Since 645 > 8, we apply the division lemma to 645 and 8, to get

645 = 8 x 80 + 5

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get

8 = 5 x 1 + 3

Step 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 8 and 645 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(645,8) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 296, 360, 645 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 296, 360, 645?

Answer: HCF of 296, 360, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 296, 360, 645 using Euclid's Algorithm?

Answer: For arbitrary numbers 296, 360, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.