How to Find GCF of 1463/234, 5516/2228?

GCF of 1463/234, 5516/2228

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 1463/234, 5516/2228 i.e 7/260676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1463/234, 5516/2228.

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 1463/234,5516/2228?

Given fractions are 1463/234,5516/2228

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 1463/234,5516/2228, numerators are 1463,5516

Denominators are 234,2228

The GCF of 1463,5516 is 7 .

LCM of 234,2228 is 260676.

The greatest common factor of 1463/234,5516/2228 = [GCF of 1463,5516]/[LCM of 234,2228]= 7/260676

Therefore, the GCF of 1463/234,5516/2228 is 7/260676.

Greatest Common Factor of 1463,5516

To find the highest common factor of 1463,5516, we have to find the factors of both numbers and list the highest common factor.

The factors of 1463 are 1, 7, 11, 19, 77, 133, 209, 1463

The factors of 5516 are 1, 2, 4, 7, 14, 28, 197, 394, 788, 1379, 2758, 5516

The HCF of 1463,5516 is 7.

Lets's calculate GCF of 1463,5516

Greatest Common Factor (GCF) of 1463,5516 By Common Division

7	1463, 5516
	209, 788

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 1463,5516 By Matching Biggest Common Factor Method

Now, list down the factors of 1463

1,7,11,19,77,133,209,1463

Now, list down the factors of 5516

1,2,4,7,14,28,197,394,788,1379,2758,5516

Greatest Common Factor

We found the factors 1463,5516 . The biggest common factor number is the GCF number.
So the greatest common factor 1463,5516 is 7.

Lets's calculate LCM of 234,2228

Lowest Common Multiple of 234,2228 using Common Division

2	234, 2228
	117, 1114

∴ So the LCM of the given numbers is 2 x 117 x 1114 = 260676

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/260676

Therefore, the GCF of Fractions 1463/234,5516/2228 is 7/260676

Least Common Multiple of 234,2228 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 234,2228 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(234,2228) = 2

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

GCF(234,2228) x common factors =2 x 1 = 2

LCM(234,2228) = ( 234 × 2228 ) / 2

LCM(234,2228) = 521352 / 2

LCM(234,2228) = 260676

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 1463/234, 5516/2228

1. What is the HCF of 1463,5516?

The HCF of 1463,5516 is 7

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 1463/234, 5516/2228?

Answer: GCF of Numerators as per given numbers 1463/234, 5516/2228 is

GCF of Numerators i.e. for 1463,5516 is 7

LCM of denominators i.e. for 234,2228 is 260676.

Thus, GCF of Fractions is 7/260676.Finally, GCF of Fractions for 1463/234, 5516/2228 is 7/260676.