How to Find GCF of 126/65, 114/5746?

GCF of 126/65, 114/5746

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 126/65, 114/5746 i.e 6/28730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 126/65, 114/5746.

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 126/65,114/5746?

Given fractions are 126/65,114/5746

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 126/65,114/5746, numerators are 126,114

Denominators are 65,5746

The GCF of 126,114 is 6 .

LCM of 65,5746 is 28730.

The greatest common factor of 126/65,114/5746 = [GCF of 126,114]/[LCM of 65,5746]= 6/28730

Therefore, the GCF of 126/65,114/5746 is 6/28730.

Greatest Common Factor of 126,114

To find the highest common factor of 126,114, we have to find the factors of both numbers and list the highest common factor.

The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114

The HCF of 126,114 is 6.

Lets's calculate GCF of 126,114

Greatest Common Factor (GCF) of 126,114 By Common Division

2	126, 114
3	63, 57
	21, 19

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 126,114 By Matching Biggest Common Factor Method

Now, list down the factors of 126

1,2,3,6,7,9,14,18,21,42,63,126

Now, list down the factors of 114

1,2,3,6,19,38,57,114

Greatest Common Factor

We found the factors 126,114 . The biggest common factor number is the GCF number.
So the greatest common factor 126,114 is 6.

Lets's calculate LCM of 65,5746

Lowest Common Multiple of 65,5746 using Common Division

13	65, 5746
	5, 442

∴ So the LCM of the given numbers is 13 x 5 x 442 = 28730

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/28730

Therefore, the GCF of Fractions 126/65,114/5746 is 6/28730

Least Common Multiple of 65,5746 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 65,5746 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,5746) = 13

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

GCF(65,5746) x common factors =13 x 1 = 13

LCM(65,5746) = ( 65 × 5746 ) / 13

LCM(65,5746) = 373490 / 13

LCM(65,5746) = 28730

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FAQs on GCF of Fractions of 126/65, 114/5746

1. What is the HCF of 126,114?

The HCF of 126,114 is 6

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 126/65, 114/5746?

Answer: GCF of Numerators as per given numbers 126/65, 114/5746 is

GCF of Numerators i.e. for 126,114 is 6

LCM of denominators i.e. for 65,5746 is 28730.

Thus, GCF of Fractions is 6/28730.Finally, GCF of Fractions for 126/65, 114/5746 is 6/28730.