How to Find GCF of 75/151, 31/661, 711/829?

GCF of 75/151, 31/661, 711/829

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 75/151, 31/661, 711/829 i.e 1/82743319 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/151, 31/661, 711/829.

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 75/151,31/661,711/829?

Given fractions are 75/151,31/661,711/829

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 75/151,31/661,711/829, numerators are 75,31,711

Denominators are 151,661,829

The GCF of 75,31,711 is 1 .

LCM of 151,661,829 is 82743319.

The greatest common factor of 75/151,31/661,711/829 = [GCF of 75,31,711]/[LCM of 151,661,829]= 1/82743319

Therefore, the GCF of 75/151,31/661,711/829 is 1/82743319.

Greatest Common Factor of 75,31,711

To find the highest common factor of 75,31,711, we have to find the factors of both numbers and list the highest common factor.

The factors of 75 are 1, 3, 5, 15, 25, 75

The factors of 31 are 1, 31

The factors of 711 are 1, 3, 9, 79, 237, 711

The HCF of 75,31,711 is 1.

Lets's calculate GCF of 75,31,711

Greatest Common Factor (GCF) of 75,31,711 By Common Division

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

Greatest Common Factor of 75,31,711 By Matching Biggest Common Factor Method

Now, list down the factors of 75

1,3,5,15,25,75

Now, list down the factors of 31

1,31

Now, list down the factors of 711

1,3,9,79,237,711

Greatest Common Factor

We found the factors 75,31,711 . The biggest common factor number is the GCF number.
So the greatest common factor 75,31,711 is 1.

Lets's calculate LCM of 151,661,829

Lowest Common Multiple of 151,661,829 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 82743319

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/82743319

Therefore, the GCF of Fractions 75/151,31/661,711/829 is 1/82743319

Least Common Multiple of 151,661,829 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 151,661,829 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(151,661,829) = 1

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

GCF(151,661,829) x common factors =1 x 1 = 1

LCM(151,661,829) = ( 151 × 661 × 829 ) / 1

LCM(151,661,829) = 82743319 / 1

LCM(151,661,829) = 82743319

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 75/151, 31/661, 711/829

1. What is the HCF of 75,31,711?

The HCF of 75,31,711 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 75/151, 31/661, 711/829?

Answer: GCF of Numerators as per given numbers 75/151, 31/661, 711/829 is

GCF of Numerators i.e. for 75,31,711 is 1

LCM of denominators i.e. for 151,661,829 is 82743319.

Thus, GCF of Fractions is 1/82743319.Finally, GCF of Fractions for 75/151, 31/661, 711/829 is 1/82743319.