How to Find GCF of 308/542, 5424/1072?

GCF of 308/542, 5424/1072

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 308/542, 5424/1072 i.e 4/290512 easily. The following is the detailed procedure to determine the greatest common factor of fractions 308/542, 5424/1072.

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 308/542,5424/1072?

Given fractions are 308/542,5424/1072

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 308/542,5424/1072, numerators are 308,5424

Denominators are 542,1072

The GCF of 308,5424 is 4 .

LCM of 542,1072 is 290512.

The greatest common factor of 308/542,5424/1072 = [GCF of 308,5424]/[LCM of 542,1072]= 4/290512

Therefore, the GCF of 308/542,5424/1072 is 4/290512.

Greatest Common Factor of 308,5424

To find the highest common factor of 308,5424, we have to find the factors of both numbers and list the highest common factor.

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

The factors of 5424 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 113, 226, 339, 452, 678, 904, 1356, 1808, 2712, 5424

The HCF of 308,5424 is 4.

Lets's calculate GCF of 308,5424

Greatest Common Factor (GCF) of 308,5424 By Common Division

2	308, 5424
2	154, 2712
	77, 1356

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 308,5424 By Matching Biggest Common Factor Method

Now, list down the factors of 308

1,2,4,7,11,14,22,28,44,77,154,308

Now, list down the factors of 5424

1,2,3,4,6,8,12,16,24,48,113,226,339,452,678,904,1356,1808,2712,5424

Greatest Common Factor

We found the factors 308,5424 . The biggest common factor number is the GCF number.
So the greatest common factor 308,5424 is 4.

Lets's calculate LCM of 542,1072

Lowest Common Multiple of 542,1072 using Common Division

2	542, 1072
	271, 536

∴ So the LCM of the given numbers is 2 x 271 x 536 = 290512

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/290512

Therefore, the GCF of Fractions 308/542,5424/1072 is 4/290512

Least Common Multiple of 542,1072 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 542,1072 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(542,1072) = 2

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

GCF(542,1072) x common factors =2 x 1 = 2

LCM(542,1072) = ( 542 × 1072 ) / 2

LCM(542,1072) = 581024 / 2

LCM(542,1072) = 290512

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FAQs on GCF of Fractions of 308/542, 5424/1072

1. What is the HCF of 308,5424?

The HCF of 308,5424 is 4

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 308/542, 5424/1072?

Answer: GCF of Numerators as per given numbers 308/542, 5424/1072 is

GCF of Numerators i.e. for 308,5424 is 4

LCM of denominators i.e. for 542,1072 is 290512.

Thus, GCF of Fractions is 4/290512.Finally, GCF of Fractions for 308/542, 5424/1072 is 4/290512.