How to Find GCF of 120/53, 208/144?

GCF of 120/53, 208/144

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 120/53, 208/144 i.e 8/7632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/53, 208/144.

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 120/53,208/144?

Given fractions are 120/53,208/144

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 120/53,208/144, numerators are 120,208

Denominators are 53,144

The GCF of 120,208 is 8 .

LCM of 53,144 is 7632.

The greatest common factor of 120/53,208/144 = [GCF of 120,208]/[LCM of 53,144]= 8/7632

Therefore, the GCF of 120/53,208/144 is 8/7632.

Greatest Common Factor of 120,208

To find the highest common factor of 120,208, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 120,208 is 8.

Lets's calculate GCF of 120,208

Greatest Common Factor (GCF) of 120,208 By Common Division

2	120, 208
2	60, 104
2	30, 52
	15, 26

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 120,208 By Matching Biggest Common Factor Method

Now, list down the factors of 120

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

Now, list down the factors of 208

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 120,208 . The biggest common factor number is the GCF number.
So the greatest common factor 120,208 is 8.

Lets's calculate LCM of 53,144

Lowest Common Multiple of 53,144 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 7632

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/7632

Therefore, the GCF of Fractions 120/53,208/144 is 8/7632

Least Common Multiple of 53,144 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 53,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(53,144) = 1

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

GCF(53,144) x common factors =1 x 1 = 1

LCM(53,144) = ( 53 × 144 ) / 1

LCM(53,144) = 7632 / 1

LCM(53,144) = 7632

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FAQs on GCF of Fractions of 120/53, 208/144

1. What is the HCF of 120,208?

The HCF of 120,208 is 8

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 120/53, 208/144?

Answer: GCF of Numerators as per given numbers 120/53, 208/144 is

GCF of Numerators i.e. for 120,208 is 8

LCM of denominators i.e. for 53,144 is 7632.

Thus, GCF of Fractions is 8/7632.Finally, GCF of Fractions for 120/53, 208/144 is 8/7632.