How to Find GCF of 127/70, 120/1140?

GCF of 127/70, 120/1140

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 127/70, 120/1140 i.e 1/7980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 127/70, 120/1140.

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 127/70,120/1140?

Given fractions are 127/70,120/1140

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 127/70,120/1140, numerators are 127,120

Denominators are 70,1140

The GCF of 127,120 is 1 .

LCM of 70,1140 is 7980.

The greatest common factor of 127/70,120/1140 = [GCF of 127,120]/[LCM of 70,1140]= 1/7980

Therefore, the GCF of 127/70,120/1140 is 1/7980.

Greatest Common Factor of 127,120

To find the highest common factor of 127,120, we have to find the factors of both numbers and list the highest common factor.

The factors of 127 are 1, 127

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The HCF of 127,120 is 1.

Lets's calculate GCF of 127,120

Greatest Common Factor (GCF) of 127,120 By Common Division

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

Greatest Common Factor of 127,120 By Matching Biggest Common Factor Method

Now, list down the factors of 127

1,127

Now, list down the factors of 120

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Greatest Common Factor

We found the factors 127,120 . The biggest common factor number is the GCF number.
So the greatest common factor 127,120 is 1.

Lets's calculate LCM of 70,1140

Lowest Common Multiple of 70,1140 using Common Division

2	70, 1140
5	35, 570
	7, 114

∴ So the LCM of the given numbers is 2 x 5 x 7 x 114 = 7980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7980

Therefore, the GCF of Fractions 127/70,120/1140 is 1/7980

Least Common Multiple of 70,1140 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 70,1140 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(70,1140) = 10

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

GCF(70,1140) x common factors =10 x 1 = 10

LCM(70,1140) = ( 70 × 1140 ) / 10

LCM(70,1140) = 79800 / 10

LCM(70,1140) = 7980

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FAQs on GCF of Fractions of 127/70, 120/1140

1. What is the HCF of 127,120?

The HCF of 127,120 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 127/70, 120/1140?

Answer: GCF of Numerators as per given numbers 127/70, 120/1140 is

GCF of Numerators i.e. for 127,120 is 1

LCM of denominators i.e. for 70,1140 is 7980.

Thus, GCF of Fractions is 1/7980.Finally, GCF of Fractions for 127/70, 120/1140 is 1/7980.