How to Find GCF of 78/220, 83/307, 278/110?

GCF of 78/220, 83/307, 278/110

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 78/220, 83/307, 278/110 i.e 1/67540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/220, 83/307, 278/110.

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 78/220,83/307,278/110?

Given fractions are 78/220,83/307,278/110

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 78/220,83/307,278/110, numerators are 78,83,278

Denominators are 220,307,110

The GCF of 78,83,278 is 1 .

LCM of 220,307,110 is 67540.

The greatest common factor of 78/220,83/307,278/110 = [GCF of 78,83,278]/[LCM of 220,307,110]= 1/67540

Therefore, the GCF of 78/220,83/307,278/110 is 1/67540.

Greatest Common Factor of 78,83,278

To find the highest common factor of 78,83,278, 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 83 are 1, 83

The factors of 278 are 1, 2, 139, 278

The HCF of 78,83,278 is 1.

Lets's calculate GCF of 78,83,278

Greatest Common Factor (GCF) of 78,83,278 By Common Division

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

Greatest Common Factor of 78,83,278 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 83

1,83

Now, list down the factors of 278

1,2,139,278

Greatest Common Factor

We found the factors 78,83,278 . The biggest common factor number is the GCF number.
So the greatest common factor 78,83,278 is 1.

Lets's calculate LCM of 220,307,110

Lowest Common Multiple of 220,307,110 using Common Division

2	220, 307, 110
5	110, 307, 55
11	22, 307, 11
	2, 307, 1

∴ So the LCM of the given numbers is 2 x 5 x 11 x 2 x 307 x 1 = 67540

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/67540

Therefore, the GCF of Fractions 78/220,83/307,278/110 is 1/67540

Least Common Multiple of 220,307,110 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 220,307,110 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(220,307,110) = 1

common factors(in case of two or more numbers have common factors) = 110

GCF(220,307,110) x common factors =1 x 110 = 110

LCM(220,307,110) = ( 220 × 307 × 110 ) / 110

LCM(220,307,110) = 7429400 / 110

LCM(220,307,110) = 67540

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FAQs on GCF of Fractions of 78/220, 83/307, 278/110

1. What is the HCF of 78,83,278?

The HCF of 78,83,278 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 78/220, 83/307, 278/110?

Answer: GCF of Numerators as per given numbers 78/220, 83/307, 278/110 is

GCF of Numerators i.e. for 78,83,278 is 1

LCM of denominators i.e. for 220,307,110 is 67540.

Thus, GCF of Fractions is 1/67540.Finally, GCF of Fractions for 78/220, 83/307, 278/110 is 1/67540.