Highest Common Factor of 199, 923, 163 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 199, 923, 163 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 199, 923, 163 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 199, 923, 163 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 199, 923, 163 is 1.

HCF(199, 923, 163) = 1

HCF of 199, 923, 163 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 199, 923, 163 is 1.

Highest Common Factor of 199,923,163 using Euclid's algorithm

Highest Common Factor of 199,923,163 is 1

Step 1: Since 923 > 199, we apply the division lemma to 923 and 199, to get

923 = 199 x 4 + 127

Step 2: Since the reminder 199 ≠ 0, we apply division lemma to 127 and 199, to get

199 = 127 x 1 + 72

Step 3: We consider the new divisor 127 and the new remainder 72, and apply the division lemma to get

127 = 72 x 1 + 55

We consider the new divisor 72 and the new remainder 55,and apply the division lemma to get

72 = 55 x 1 + 17

We consider the new divisor 55 and the new remainder 17,and apply the division lemma to get

55 = 17 x 3 + 4

We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get

17 = 4 x 4 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 199 and 923 is 1

Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(55,17) = HCF(72,55) = HCF(127,72) = HCF(199,127) = HCF(923,199) .

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

Step 1: Since 163 > 1, we apply the division lemma to 163 and 1, to get

163 = 1 x 163 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 163 is 1

Notice that 1 = HCF(163,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 199, 923, 163 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 199, 923, 163?

Answer: HCF of 199, 923, 163 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 199, 923, 163 using Euclid's Algorithm?

Answer: For arbitrary numbers 199, 923, 163 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.