How to Find GCF of 40/78, 42/176, 620/296?

GCF of 40/78, 42/176, 620/296

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 40/78, 42/176, 620/296 i.e 2/253968 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/78, 42/176, 620/296.

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 40/78,42/176,620/296?

Given fractions are 40/78,42/176,620/296

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 40/78,42/176,620/296, numerators are 40,42,620

Denominators are 78,176,296

The GCF of 40,42,620 is 2 .

LCM of 78,176,296 is 253968.

The greatest common factor of 40/78,42/176,620/296 = [GCF of 40,42,620]/[LCM of 78,176,296]= 2/253968

Therefore, the GCF of 40/78,42/176,620/296 is 2/253968.

Greatest Common Factor of 40,42,620

To find the highest common factor of 40,42,620, we have to find the factors of both numbers and list the highest common factor.

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

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

The factors of 620 are 1, 2, 4, 5, 10, 20, 31, 62, 124, 155, 310, 620

The HCF of 40,42,620 is 2.

Lets's calculate GCF of 40,42,620

Greatest Common Factor (GCF) of 40,42,620 By Common Division

2	40, 42, 620
	20, 21, 310

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

Greatest Common Factor of 40,42,620 By Matching Biggest Common Factor Method

Now, list down the factors of 40

1,2,4,5,8,10,20,40

Now, list down the factors of 42

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

Now, list down the factors of 620

1,2,4,5,10,20,31,62,124,155,310,620

Greatest Common Factor

We found the factors 40,42,620 . The biggest common factor number is the GCF number.
So the greatest common factor 40,42,620 is 2.

Lets's calculate LCM of 78,176,296

Lowest Common Multiple of 78,176,296 using Common Division

2	78, 176, 296
2	39, 88, 148
2	39, 44, 74
	39, 22, 37

∴ So the LCM of the given numbers is 2 x 2 x 2 x 39 x 22 x 37 = 253968

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/253968

Therefore, the GCF of Fractions 40/78,42/176,620/296 is 2/253968

Least Common Multiple of 78,176,296 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 78,176,296 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,176,296) = 2

common factors(in case of two or more numbers have common factors) = 8

GCF(78,176,296) x common factors =2 x 8 = 16

LCM(78,176,296) = ( 78 × 176 × 296 ) / 16

LCM(78,176,296) = 4063488 / 16

LCM(78,176,296) = 253968

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 40/78, 42/176, 620/296

1. What is the HCF of 40,42,620?

The HCF of 40,42,620 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 40/78, 42/176, 620/296?

Answer: GCF of Numerators as per given numbers 40/78, 42/176, 620/296 is

GCF of Numerators i.e. for 40,42,620 is 2

LCM of denominators i.e. for 78,176,296 is 253968.

Thus, GCF of Fractions is 2/253968.Finally, GCF of Fractions for 40/78, 42/176, 620/296 is 2/253968.