Highest Common Factor of 223, 368, 369 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, 368, 369 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 223, 368, 369 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, 368, 369 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, 368, 369 is 1.

HCF(223, 368, 369) = 1

HCF of 223, 368, 369 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, 368, 369 is 1.

Highest Common Factor of 223,368,369 using Euclid's algorithm

Highest Common Factor of 223,368,369 is 1

Step 1: Since 368 > 223, we apply the division lemma to 368 and 223, to get

368 = 223 x 1 + 145

Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 145 and 223, to get

223 = 145 x 1 + 78

Step 3: We consider the new divisor 145 and the new remainder 78, and apply the division lemma to get

145 = 78 x 1 + 67

We consider the new divisor 78 and the new remainder 67,and apply the division lemma to get

78 = 67 x 1 + 11

We consider the new divisor 67 and the new remainder 11,and apply the division lemma to get

67 = 11 x 6 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 223 and 368 is 1

Notice that 1 = HCF(11,1) = HCF(67,11) = HCF(78,67) = HCF(145,78) = HCF(223,145) = HCF(368,223) .

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

Step 1: Since 369 > 1, we apply the division lemma to 369 and 1, to get

369 = 1 x 369 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 369 is 1

Notice that 1 = HCF(369,1) .

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, 368, 369 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, 368, 369?

Answer: HCF of 223, 368, 369 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 223, 368, 369 using Euclid's Algorithm?

Answer: For arbitrary numbers 223, 368, 369 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.