How to Find GCF of 504/856, 108/749?

GCF of 504/856, 108/749

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 504/856, 108/749 i.e 36/5992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 504/856, 108/749.

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 504/856,108/749?

Given fractions are 504/856,108/749

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 504/856,108/749, numerators are 504,108

Denominators are 856,749

The GCF of 504,108 is 36 .

LCM of 856,749 is 5992.

The greatest common factor of 504/856,108/749 = [GCF of 504,108]/[LCM of 856,749]= 36/5992

Therefore, the GCF of 504/856,108/749 is 36/5992.

Greatest Common Factor of 504,108

To find the highest common factor of 504,108, we have to find the factors of both numbers and list the highest common factor.

The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504

The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The HCF of 504,108 is 36.

Lets's calculate GCF of 504,108

Greatest Common Factor (GCF) of 504,108 By Common Division

2	504, 108
2	252, 54
3	126, 27
3	42, 9
	14, 3

∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36

Greatest Common Factor of 504,108 By Matching Biggest Common Factor Method

Now, list down the factors of 504

1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504

Now, list down the factors of 108

1,2,3,4,6,9,12,18,27,36,54,108

Greatest Common Factor

We found the factors 504,108 . The biggest common factor number is the GCF number.
So the greatest common factor 504,108 is 36.

Lets's calculate LCM of 856,749

Lowest Common Multiple of 856,749 using Common Division

107	856, 749
	8, 7

∴ So the LCM of the given numbers is 107 x 8 x 7 = 5992

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/5992

Therefore, the GCF of Fractions 504/856,108/749 is 36/5992

Least Common Multiple of 856,749 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 856,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(856,749) = 107

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

GCF(856,749) x common factors =107 x 1 = 107

LCM(856,749) = ( 856 × 749 ) / 107

LCM(856,749) = 641144 / 107

LCM(856,749) = 5992

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FAQs on GCF of Fractions of 504/856, 108/749

1. What is the HCF of 504,108?

The HCF of 504,108 is 36

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 504/856, 108/749?

Answer: GCF of Numerators as per given numbers 504/856, 108/749 is

GCF of Numerators i.e. for 504,108 is 36

LCM of denominators i.e. for 856,749 is 5992.

Thus, GCF of Fractions is 36/5992.Finally, GCF of Fractions for 504/856, 108/749 is 36/5992.