Highest Common Factor of 354, 631, 193 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 354, 631, 193 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 631, 193 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 354, 631, 193 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 354, 631, 193 is 1.

HCF(354, 631, 193) = 1

HCF of 354, 631, 193 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 354, 631, 193 is 1.

Highest Common Factor of 354,631,193 using Euclid's algorithm

Highest Common Factor of 354,631,193 is 1

Step 1: Since 631 > 354, we apply the division lemma to 631 and 354, to get

631 = 354 x 1 + 277

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 277 and 354, to get

354 = 277 x 1 + 77

Step 3: We consider the new divisor 277 and the new remainder 77, and apply the division lemma to get

277 = 77 x 3 + 46

We consider the new divisor 77 and the new remainder 46,and apply the division lemma to get

77 = 46 x 1 + 31

We consider the new divisor 46 and the new remainder 31,and apply the division lemma to get

46 = 31 x 1 + 15

We consider the new divisor 31 and the new remainder 15,and apply the division lemma to get

31 = 15 x 2 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 354 and 631 is 1

Notice that 1 = HCF(15,1) = HCF(31,15) = HCF(46,31) = HCF(77,46) = HCF(277,77) = HCF(354,277) = HCF(631,354) .

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

Step 1: Since 193 > 1, we apply the division lemma to 193 and 1, to get

193 = 1 x 193 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 193 is 1

Notice that 1 = HCF(193,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 354, 631, 193 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 354, 631, 193?

Answer: HCF of 354, 631, 193 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 631, 193 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 631, 193 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.