How to Find GCF of 756/488, 198/596?

GCF of 756/488, 198/596

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 756/488, 198/596 i.e 18/72712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 756/488, 198/596.

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 756/488,198/596?

Given fractions are 756/488,198/596

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 756/488,198/596, numerators are 756,198

Denominators are 488,596

The GCF of 756,198 is 18 .

LCM of 488,596 is 72712.

The greatest common factor of 756/488,198/596 = [GCF of 756,198]/[LCM of 488,596]= 18/72712

Therefore, the GCF of 756/488,198/596 is 18/72712.

Greatest Common Factor of 756,198

To find the highest common factor of 756,198, we have to find the factors of both numbers and list the highest common factor.

The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

The HCF of 756,198 is 18.

Lets's calculate GCF of 756,198

Greatest Common Factor (GCF) of 756,198 By Common Division

2	756, 198
3	378, 99
3	126, 33
	42, 11

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 756,198 By Matching Biggest Common Factor Method

Now, list down the factors of 756

1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756

Now, list down the factors of 198

1,2,3,6,9,11,18,22,33,66,99,198

Greatest Common Factor

We found the factors 756,198 . The biggest common factor number is the GCF number.
So the greatest common factor 756,198 is 18.

Lets's calculate LCM of 488,596

Lowest Common Multiple of 488,596 using Common Division

2	488, 596
2	244, 298
	122, 149

∴ So the LCM of the given numbers is 2 x 2 x 122 x 149 = 72712

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/72712

Therefore, the GCF of Fractions 756/488,198/596 is 18/72712

Least Common Multiple of 488,596 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 488,596 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(488,596) = 4

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

GCF(488,596) x common factors =4 x 1 = 4

LCM(488,596) = ( 488 × 596 ) / 4

LCM(488,596) = 290848 / 4

LCM(488,596) = 72712

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FAQs on GCF of Fractions of 756/488, 198/596

1. What is the HCF of 756,198?

The HCF of 756,198 is 18

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 756/488, 198/596?

Answer: GCF of Numerators as per given numbers 756/488, 198/596 is

GCF of Numerators i.e. for 756,198 is 18

LCM of denominators i.e. for 488,596 is 72712.

Thus, GCF of Fractions is 18/72712.Finally, GCF of Fractions for 756/488, 198/596 is 18/72712.