How to Find GCF of 768/812, 308/251?

GCF of 768/812, 308/251

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 768/812, 308/251 i.e 4/203812 easily. The following is the detailed procedure to determine the greatest common factor of fractions 768/812, 308/251.

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 768/812,308/251?

Given fractions are 768/812,308/251

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 768/812,308/251, numerators are 768,308

Denominators are 812,251

The GCF of 768,308 is 4 .

LCM of 812,251 is 203812.

The greatest common factor of 768/812,308/251 = [GCF of 768,308]/[LCM of 812,251]= 4/203812

Therefore, the GCF of 768/812,308/251 is 4/203812.

Greatest Common Factor of 768,308

To find the highest common factor of 768,308, we have to find the factors of both numbers and list the highest common factor.

The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768

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

The HCF of 768,308 is 4.

Lets's calculate GCF of 768,308

Greatest Common Factor (GCF) of 768,308 By Common Division

2	768, 308
2	384, 154
	192, 77

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

Greatest Common Factor of 768,308 By Matching Biggest Common Factor Method

Now, list down the factors of 768

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Now, list down the factors of 308

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

Greatest Common Factor

We found the factors 768,308 . The biggest common factor number is the GCF number.
So the greatest common factor 768,308 is 4.

Lets's calculate LCM of 812,251

Lowest Common Multiple of 812,251 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 203812

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/203812

Therefore, the GCF of Fractions 768/812,308/251 is 4/203812

Least Common Multiple of 812,251 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 812,251 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(812,251) = 1

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

GCF(812,251) x common factors =1 x 1 = 1

LCM(812,251) = ( 812 × 251 ) / 1

LCM(812,251) = 203812 / 1

LCM(812,251) = 203812

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FAQs on GCF of Fractions of 768/812, 308/251

1. What is the HCF of 768,308?

The HCF of 768,308 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 768/812, 308/251?

Answer: GCF of Numerators as per given numbers 768/812, 308/251 is

GCF of Numerators i.e. for 768,308 is 4

LCM of denominators i.e. for 812,251 is 203812.

Thus, GCF of Fractions is 4/203812.Finally, GCF of Fractions for 768/812, 308/251 is 4/203812.