How to Find GCF of 740/64, 260/304?

GCF of 740/64, 260/304

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 740/64, 260/304 i.e 20/1216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 740/64, 260/304.

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 740/64,260/304?

Given fractions are 740/64,260/304

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 740/64,260/304, numerators are 740,260

Denominators are 64,304

The GCF of 740,260 is 20 .

LCM of 64,304 is 1216.

The greatest common factor of 740/64,260/304 = [GCF of 740,260]/[LCM of 64,304]= 20/1216

Therefore, the GCF of 740/64,260/304 is 20/1216.

Greatest Common Factor of 740,260

To find the highest common factor of 740,260, we have to find the factors of both numbers and list the highest common factor.

The factors of 740 are 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740

The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260

The HCF of 740,260 is 20.

Lets's calculate GCF of 740,260

Greatest Common Factor (GCF) of 740,260 By Common Division

2	740, 260
2	370, 130
5	185, 65
	37, 13

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 740,260 By Matching Biggest Common Factor Method

Now, list down the factors of 740

1,2,4,5,10,20,37,74,148,185,370,740

Now, list down the factors of 260

1,2,4,5,10,13,20,26,52,65,130,260

Greatest Common Factor

We found the factors 740,260 . The biggest common factor number is the GCF number.
So the greatest common factor 740,260 is 20.

Lets's calculate LCM of 64,304

Lowest Common Multiple of 64,304 using Common Division

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

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 4 x 19 = 1216

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/1216

Therefore, the GCF of Fractions 740/64,260/304 is 20/1216

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

GCF(64,304) = 16

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

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

LCM(64,304) = ( 64 × 304 ) / 16

LCM(64,304) = 19456 / 16

LCM(64,304) = 1216

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FAQs on GCF of Fractions of 740/64, 260/304

1. What is the HCF of 740,260?

The HCF of 740,260 is 20

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 740/64, 260/304?

Answer: GCF of Numerators as per given numbers 740/64, 260/304 is

GCF of Numerators i.e. for 740,260 is 20

LCM of denominators i.e. for 64,304 is 1216.

Thus, GCF of Fractions is 20/1216.Finally, GCF of Fractions for 740/64, 260/304 is 20/1216.