How to Find GCF of 78/132, 37/959, 188/821?

GCF of 78/132, 37/959, 188/821

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 78/132, 37/959, 188/821 i.e 1/103928748 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/132, 37/959, 188/821.

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 78/132,37/959,188/821?

Given fractions are 78/132,37/959,188/821

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 78/132,37/959,188/821, numerators are 78,37,188

Denominators are 132,959,821

The GCF of 78,37,188 is 1 .

LCM of 132,959,821 is 103928748.

The greatest common factor of 78/132,37/959,188/821 = [GCF of 78,37,188]/[LCM of 132,959,821]= 1/103928748

Therefore, the GCF of 78/132,37/959,188/821 is 1/103928748.

Greatest Common Factor of 78,37,188

To find the highest common factor of 78,37,188, we have to find the factors of both numbers and list the highest common factor.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The factors of 37 are 1, 37

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

The HCF of 78,37,188 is 1.

Lets's calculate GCF of 78,37,188

Greatest Common Factor (GCF) of 78,37,188 By Common Division

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

Greatest Common Factor of 78,37,188 By Matching Biggest Common Factor Method

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 37

1,37

Now, list down the factors of 188

1,2,4,47,94,188

Greatest Common Factor

We found the factors 78,37,188 . The biggest common factor number is the GCF number.
So the greatest common factor 78,37,188 is 1.

Lets's calculate LCM of 132,959,821

Lowest Common Multiple of 132,959,821 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 103928748

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/103928748

Therefore, the GCF of Fractions 78/132,37/959,188/821 is 1/103928748

Least Common Multiple of 132,959,821 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 132,959,821 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(132,959,821) = 1

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

GCF(132,959,821) x common factors =1 x 1 = 1

LCM(132,959,821) = ( 132 × 959 × 821 ) / 1

LCM(132,959,821) = 103928748 / 1

LCM(132,959,821) = 103928748

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 78/132, 37/959, 188/821

1. What is the HCF of 78,37,188?

The HCF of 78,37,188 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 78/132, 37/959, 188/821?

Answer: GCF of Numerators as per given numbers 78/132, 37/959, 188/821 is

GCF of Numerators i.e. for 78,37,188 is 1

LCM of denominators i.e. for 132,959,821 is 103928748.

Thus, GCF of Fractions is 1/103928748.Finally, GCF of Fractions for 78/132, 37/959, 188/821 is 1/103928748.