How to Find GCF of 60/38, 14/32, 188/751?

GCF of 60/38, 14/32, 188/751

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 60/38, 14/32, 188/751 i.e 2/456608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/38, 14/32, 188/751.

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 60/38,14/32,188/751?

Given fractions are 60/38,14/32,188/751

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 60/38,14/32,188/751, numerators are 60,14,188

Denominators are 38,32,751

The GCF of 60,14,188 is 2 .

LCM of 38,32,751 is 456608.

The greatest common factor of 60/38,14/32,188/751 = [GCF of 60,14,188]/[LCM of 38,32,751]= 2/456608

Therefore, the GCF of 60/38,14/32,188/751 is 2/456608.

Greatest Common Factor of 60,14,188

To find the highest common factor of 60,14,188, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 14 are 1, 2, 7, 14

The factors of 188 are 1, 2, 4, 47, 94, 188

The HCF of 60,14,188 is 2.

Lets's calculate GCF of 60,14,188

Greatest Common Factor (GCF) of 60,14,188 By Common Division

2	60, 14, 188
	30, 7, 94

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

Greatest Common Factor of 60,14,188 By Matching Biggest Common Factor Method

Now, list down the factors of 60

1,2,3,4,5,6,10,12,15,20,30,60

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 188

1,2,4,47,94,188

Greatest Common Factor

We found the factors 60,14,188 . The biggest common factor number is the GCF number.
So the greatest common factor 60,14,188 is 2.

Lets's calculate LCM of 38,32,751

Lowest Common Multiple of 38,32,751 using Common Division

2	38, 32, 751
	19, 16, 751

∴ So the LCM of the given numbers is 2 x 19 x 16 x 751 = 456608

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/456608

Therefore, the GCF of Fractions 60/38,14/32,188/751 is 2/456608

Least Common Multiple of 38,32,751 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 38,32,751 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,32,751) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(38,32,751) x common factors =1 x 2 = 2

LCM(38,32,751) = ( 38 × 32 × 751 ) / 2

LCM(38,32,751) = 913216 / 2

LCM(38,32,751) = 456608

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 60/38, 14/32, 188/751

1. What is the HCF of 60,14,188?

The HCF of 60,14,188 is 2

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 60/38, 14/32, 188/751?

Answer: GCF of Numerators as per given numbers 60/38, 14/32, 188/751 is

GCF of Numerators i.e. for 60,14,188 is 2

LCM of denominators i.e. for 38,32,751 is 456608.

Thus, GCF of Fractions is 2/456608.Finally, GCF of Fractions for 60/38, 14/32, 188/751 is 2/456608.