How to Find GCF of 7/20, 78/768, 42/222?

GCF of 7/20, 78/768, 42/222

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 7/20, 78/768, 42/222 i.e 1/142080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7/20, 78/768, 42/222.

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 7/20,78/768,42/222?

Given fractions are 7/20,78/768,42/222

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 7/20,78/768,42/222, numerators are 7,78,42

Denominators are 20,768,222

The GCF of 7,78,42 is 1 .

LCM of 20,768,222 is 142080.

The greatest common factor of 7/20,78/768,42/222 = [GCF of 7,78,42]/[LCM of 20,768,222]= 1/142080

Therefore, the GCF of 7/20,78/768,42/222 is 1/142080.

Greatest Common Factor of 7,78,42

To find the highest common factor of 7,78,42, we have to find the factors of both numbers and list the highest common factor.

The factors of 7 are 1, 7

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

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The HCF of 7,78,42 is 1.

Lets's calculate GCF of 7,78,42

Greatest Common Factor (GCF) of 7,78,42 By Common Division

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

Greatest Common Factor of 7,78,42 By Matching Biggest Common Factor Method

Now, list down the factors of 7

1,7

Now, list down the factors of 78

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

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Greatest Common Factor

We found the factors 7,78,42 . The biggest common factor number is the GCF number.
So the greatest common factor 7,78,42 is 1.

Lets's calculate LCM of 20,768,222

Lowest Common Multiple of 20,768,222 using Common Division

2	20, 768, 222
2	10, 384, 111
3	5, 192, 111
	5, 64, 37

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 64 x 37 = 142080

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/142080

Therefore, the GCF of Fractions 7/20,78/768,42/222 is 1/142080

Least Common Multiple of 20,768,222 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 20,768,222 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,768,222) = 2

common factors(in case of two or more numbers have common factors) = 12

GCF(20,768,222) x common factors =2 x 12 = 24

LCM(20,768,222) = ( 20 × 768 × 222 ) / 24

LCM(20,768,222) = 3409920 / 24

LCM(20,768,222) = 142080

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 7/20, 78/768, 42/222

1. What is the HCF of 7,78,42?

The HCF of 7,78,42 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 7/20, 78/768, 42/222?

Answer: GCF of Numerators as per given numbers 7/20, 78/768, 42/222 is

GCF of Numerators i.e. for 7,78,42 is 1

LCM of denominators i.e. for 20,768,222 is 142080.

Thus, GCF of Fractions is 1/142080.Finally, GCF of Fractions for 7/20, 78/768, 42/222 is 1/142080.