How to Find GCF of 225/656, 1307/3688?

GCF of 225/656, 1307/3688

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 225/656, 1307/3688 i.e 1/302416 easily. The following is the detailed procedure to determine the greatest common factor of fractions 225/656, 1307/3688.

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 225/656,1307/3688?

Given fractions are 225/656,1307/3688

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 225/656,1307/3688, numerators are 225,1307

Denominators are 656,3688

The GCF of 225,1307 is 1 .

LCM of 656,3688 is 302416.

The greatest common factor of 225/656,1307/3688 = [GCF of 225,1307]/[LCM of 656,3688]= 1/302416

Therefore, the GCF of 225/656,1307/3688 is 1/302416.

Greatest Common Factor of 225,1307

To find the highest common factor of 225,1307, we have to find the factors of both numbers and list the highest common factor.

The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225

The factors of 1307 are 1, 1307

The HCF of 225,1307 is 1.

Lets's calculate GCF of 225,1307

Greatest Common Factor (GCF) of 225,1307 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 225,1307 By Matching Biggest Common Factor Method

Now, list down the factors of 225

1,3,5,9,15,25,45,75,225

Now, list down the factors of 1307

1,1307

Greatest Common Factor

We found the factors 225,1307 . The biggest common factor number is the GCF number.
So the greatest common factor 225,1307 is 1.

Lets's calculate LCM of 656,3688

Lowest Common Multiple of 656,3688 using Common Division

2	656, 3688
2	328, 1844
2	164, 922
	82, 461

∴ So the LCM of the given numbers is 2 x 2 x 2 x 82 x 461 = 302416

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/302416

Therefore, the GCF of Fractions 225/656,1307/3688 is 1/302416

Least Common Multiple of 656,3688 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 656,3688 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(656,3688) = 8

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

GCF(656,3688) x common factors =8 x 1 = 8

LCM(656,3688) = ( 656 × 3688 ) / 8

LCM(656,3688) = 2419328 / 8

LCM(656,3688) = 302416

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FAQs on GCF of Fractions of 225/656, 1307/3688

1. What is the HCF of 225,1307?

The HCF of 225,1307 is 1

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 225/656, 1307/3688?

Answer: GCF of Numerators as per given numbers 225/656, 1307/3688 is

GCF of Numerators i.e. for 225,1307 is 1

LCM of denominators i.e. for 656,3688 is 302416.

Thus, GCF of Fractions is 1/302416.Finally, GCF of Fractions for 225/656, 1307/3688 is 1/302416.