Highest Common Factor of 223, 1725, 6918 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 223, 1725, 6918 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 223, 1725, 6918 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 223, 1725, 6918 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 223, 1725, 6918 is 1.

HCF(223, 1725, 6918) = 1

HCF of 223, 1725, 6918 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 223, 1725, 6918 is 1.

Highest Common Factor of 223,1725,6918 using Euclid's algorithm

Highest Common Factor of 223,1725,6918 is 1

Step 1: Since 1725 > 223, we apply the division lemma to 1725 and 223, to get

1725 = 223 x 7 + 164

Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 164 and 223, to get

223 = 164 x 1 + 59

Step 3: We consider the new divisor 164 and the new remainder 59, and apply the division lemma to get

164 = 59 x 2 + 46

We consider the new divisor 59 and the new remainder 46,and apply the division lemma to get

59 = 46 x 1 + 13

We consider the new divisor 46 and the new remainder 13,and apply the division lemma to get

46 = 13 x 3 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 223 and 1725 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(46,13) = HCF(59,46) = HCF(164,59) = HCF(223,164) = HCF(1725,223) .

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

Step 1: Since 6918 > 1, we apply the division lemma to 6918 and 1, to get

6918 = 1 x 6918 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6918 is 1

Notice that 1 = HCF(6918,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 223, 1725, 6918 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 223, 1725, 6918?

Answer: HCF of 223, 1725, 6918 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 223, 1725, 6918 using Euclid's Algorithm?

Answer: For arbitrary numbers 223, 1725, 6918 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.