How to Find GCF of 71/65, 76/997, 414/748?

GCF of 71/65, 76/997, 414/748

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 71/65, 76/997, 414/748 i.e 1/48474140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/65, 76/997, 414/748.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 71/65,76/997,414/748?

Given fractions are 71/65,76/997,414/748

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 71/65,76/997,414/748, numerators are 71,76,414

Denominators are 65,997,748

The GCF of 71,76,414 is 1 .

LCM of 65,997,748 is 48474140.

The greatest common factor of 71/65,76/997,414/748 = [GCF of 71,76,414]/[LCM of 65,997,748]= 1/48474140

Therefore, the GCF of 71/65,76/997,414/748 is 1/48474140.

Greatest Common Factor of 71,76,414

To find the highest common factor of 71,76,414, we have to find the factors of both numbers and list the highest common factor.

The factors of 71 are 1, 71

The factors of 76 are 1, 2, 4, 19, 38, 76

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The HCF of 71,76,414 is 1.

Lets's calculate GCF of 71,76,414

Greatest Common Factor (GCF) of 71,76,414 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 71,76,414 By Matching Biggest Common Factor Method

Now, list down the factors of 71

1,71

Now, list down the factors of 76

1,2,4,19,38,76

Now, list down the factors of 414

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 71,76,414 . The biggest common factor number is the GCF number.
So the greatest common factor 71,76,414 is 1.

Lets's calculate LCM of 65,997,748

Lowest Common Multiple of 65,997,748 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 48474140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/48474140

Therefore, the GCF of Fractions 71/65,76/997,414/748 is 1/48474140

Least Common Multiple of 65,997,748 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 65,997,748 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,997,748) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(65,997,748) x common factors =1 x 1 = 1

LCM(65,997,748) = ( 65 × 997 × 748 ) / 1

LCM(65,997,748) = 48474140 / 1

LCM(65,997,748) = 48474140

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 71/65, 76/997, 414/748

1. What is the HCF of 71,76,414?

The HCF of 71,76,414 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 71/65, 76/997, 414/748?

Answer: GCF of Numerators as per given numbers 71/65, 76/997, 414/748 is

GCF of Numerators i.e. for 71,76,414 is 1

LCM of denominators i.e. for 65,997,748 is 48474140.

Thus, GCF of Fractions is 1/48474140.Finally, GCF of Fractions for 71/65, 76/997, 414/748 is 1/48474140.