How to Find GCF of 1038/692, 7322/5514?

GCF of 1038/692, 7322/5514

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 1038/692, 7322/5514 i.e 2/1907844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1038/692, 7322/5514.

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 1038/692,7322/5514?

Given fractions are 1038/692,7322/5514

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 1038/692,7322/5514, numerators are 1038,7322

Denominators are 692,5514

The GCF of 1038,7322 is 2 .

LCM of 692,5514 is 1907844.

The greatest common factor of 1038/692,7322/5514 = [GCF of 1038,7322]/[LCM of 692,5514]= 2/1907844

Therefore, the GCF of 1038/692,7322/5514 is 2/1907844.

Greatest Common Factor of 1038,7322

To find the highest common factor of 1038,7322, we have to find the factors of both numbers and list the highest common factor.

The factors of 1038 are 1, 2, 3, 6, 173, 346, 519, 1038

The factors of 7322 are 1, 2, 7, 14, 523, 1046, 3661, 7322

The HCF of 1038,7322 is 2.

Lets's calculate GCF of 1038,7322

Greatest Common Factor (GCF) of 1038,7322 By Common Division

2	1038, 7322
	519, 3661

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

Greatest Common Factor of 1038,7322 By Matching Biggest Common Factor Method

Now, list down the factors of 1038

1,2,3,6,173,346,519,1038

Now, list down the factors of 7322

1,2,7,14,523,1046,3661,7322

Greatest Common Factor

We found the factors 1038,7322 . The biggest common factor number is the GCF number.
So the greatest common factor 1038,7322 is 2.

Lets's calculate LCM of 692,5514

Lowest Common Multiple of 692,5514 using Common Division

2	692, 5514
	346, 2757

∴ So the LCM of the given numbers is 2 x 346 x 2757 = 1907844

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1907844

Therefore, the GCF of Fractions 1038/692,7322/5514 is 2/1907844

Least Common Multiple of 692,5514 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 692,5514 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(692,5514) = 2

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

GCF(692,5514) x common factors =2 x 1 = 2

LCM(692,5514) = ( 692 × 5514 ) / 2

LCM(692,5514) = 3815688 / 2

LCM(692,5514) = 1907844

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FAQs on GCF of Fractions of 1038/692, 7322/5514

1. What is the HCF of 1038,7322?

The HCF of 1038,7322 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 1038/692, 7322/5514?

Answer: GCF of Numerators as per given numbers 1038/692, 7322/5514 is

GCF of Numerators i.e. for 1038,7322 is 2

LCM of denominators i.e. for 692,5514 is 1907844.

Thus, GCF of Fractions is 2/1907844.Finally, GCF of Fractions for 1038/692, 7322/5514 is 2/1907844.