How to Find GCF of 82/69, 992/64, 274/304?

GCF of 82/69, 992/64, 274/304

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 82/69, 992/64, 274/304 i.e 2/83904 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/69, 992/64, 274/304.

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 82/69,992/64,274/304?

Given fractions are 82/69,992/64,274/304

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 82/69,992/64,274/304, numerators are 82,992,274

Denominators are 69,64,304

The GCF of 82,992,274 is 2 .

LCM of 69,64,304 is 83904.

The greatest common factor of 82/69,992/64,274/304 = [GCF of 82,992,274]/[LCM of 69,64,304]= 2/83904

Therefore, the GCF of 82/69,992/64,274/304 is 2/83904.

Greatest Common Factor of 82,992,274

To find the highest common factor of 82,992,274, we have to find the factors of both numbers and list the highest common factor.

The factors of 82 are 1, 2, 41, 82

The factors of 992 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992

The factors of 274 are 1, 2, 137, 274

The HCF of 82,992,274 is 2.

Lets's calculate GCF of 82,992,274

Greatest Common Factor (GCF) of 82,992,274 By Common Division

2	82, 992, 274
	41, 496, 137

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

Greatest Common Factor of 82,992,274 By Matching Biggest Common Factor Method

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 992

1,2,4,8,16,31,32,62,124,248,496,992

Now, list down the factors of 274

1,2,137,274

Greatest Common Factor

We found the factors 82,992,274 . The biggest common factor number is the GCF number.
So the greatest common factor 82,992,274 is 2.

Lets's calculate LCM of 69,64,304

Lowest Common Multiple of 69,64,304 using Common Division

2	69, 64, 304
2	69, 32, 152
2	69, 16, 76
2	69, 8, 38
	69, 4, 19

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 69 x 4 x 19 = 83904

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/83904

Therefore, the GCF of Fractions 82/69,992/64,274/304 is 2/83904

Least Common Multiple of 69,64,304 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 69,64,304 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(69,64,304) = 1

common factors(in case of two or more numbers have common factors) = 16

GCF(69,64,304) x common factors =1 x 16 = 16

LCM(69,64,304) = ( 69 × 64 × 304 ) / 16

LCM(69,64,304) = 1342464 / 16

LCM(69,64,304) = 83904

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FAQs on GCF of Fractions of 82/69, 992/64, 274/304

1. What is the HCF of 82,992,274?

The HCF of 82,992,274 is 2

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 82/69, 992/64, 274/304?

Answer: GCF of Numerators as per given numbers 82/69, 992/64, 274/304 is

GCF of Numerators i.e. for 82,992,274 is 2

LCM of denominators i.e. for 69,64,304 is 83904.

Thus, GCF of Fractions is 2/83904.Finally, GCF of Fractions for 82/69, 992/64, 274/304 is 2/83904.