Highest Common Factor of 734, 196, 471 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 734, 196, 471 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 734, 196, 471 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 734, 196, 471 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 734, 196, 471 is 1.

HCF(734, 196, 471) = 1

HCF of 734, 196, 471 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 734, 196, 471 is 1.

Highest Common Factor of 734,196,471 using Euclid's algorithm

Highest Common Factor of 734,196,471 is 1

Step 1: Since 734 > 196, we apply the division lemma to 734 and 196, to get

734 = 196 x 3 + 146

Step 2: Since the reminder 196 ≠ 0, we apply division lemma to 146 and 196, to get

196 = 146 x 1 + 50

Step 3: We consider the new divisor 146 and the new remainder 50, and apply the division lemma to get

146 = 50 x 2 + 46

We consider the new divisor 50 and the new remainder 46,and apply the division lemma to get

50 = 46 x 1 + 4

We consider the new divisor 46 and the new remainder 4,and apply the division lemma to get

46 = 4 x 11 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 734 and 196 is 2

Notice that 2 = HCF(4,2) = HCF(46,4) = HCF(50,46) = HCF(146,50) = HCF(196,146) = HCF(734,196) .

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

Step 1: Since 471 > 2, we apply the division lemma to 471 and 2, to get

471 = 2 x 235 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 471 is 1

Notice that 1 = HCF(2,1) = HCF(471,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 734, 196, 471 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 734, 196, 471?

Answer: HCF of 734, 196, 471 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 734, 196, 471 using Euclid's Algorithm?

Answer: For arbitrary numbers 734, 196, 471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.