How to Find GCF of 3502/274, 2414/9532?

GCF of 3502/274, 2414/9532

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 3502/274, 2414/9532 i.e 34/1305884 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3502/274, 2414/9532.

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 3502/274,2414/9532?

Given fractions are 3502/274,2414/9532

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 3502/274,2414/9532, numerators are 3502,2414

Denominators are 274,9532

The GCF of 3502,2414 is 34 .

LCM of 274,9532 is 1305884.

The greatest common factor of 3502/274,2414/9532 = [GCF of 3502,2414]/[LCM of 274,9532]= 34/1305884

Therefore, the GCF of 3502/274,2414/9532 is 34/1305884.

Greatest Common Factor of 3502,2414

To find the highest common factor of 3502,2414, we have to find the factors of both numbers and list the highest common factor.

The factors of 3502 are 1, 2, 17, 34, 103, 206, 1751, 3502

The factors of 2414 are 1, 2, 17, 34, 71, 142, 1207, 2414

The HCF of 3502,2414 is 34.

Lets's calculate GCF of 3502,2414

Greatest Common Factor (GCF) of 3502,2414 By Common Division

2	3502, 2414
17	1751, 1207
	103, 71

∴ So the GCF of the given numbers is 2 x 17 = 34

Greatest Common Factor of 3502,2414 By Matching Biggest Common Factor Method

Now, list down the factors of 3502

1,2,17,34,103,206,1751,3502

Now, list down the factors of 2414

1,2,17,34,71,142,1207,2414

Greatest Common Factor

We found the factors 3502,2414 . The biggest common factor number is the GCF number.
So the greatest common factor 3502,2414 is 34.

Lets's calculate LCM of 274,9532

Lowest Common Multiple of 274,9532 using Common Division

2	274, 9532
	137, 4766

∴ So the LCM of the given numbers is 2 x 137 x 4766 = 1305884

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/1305884

Therefore, the GCF of Fractions 3502/274,2414/9532 is 34/1305884

Least Common Multiple of 274,9532 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 274,9532 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(274,9532) = 2

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

GCF(274,9532) x common factors =2 x 1 = 2

LCM(274,9532) = ( 274 × 9532 ) / 2

LCM(274,9532) = 2611768 / 2

LCM(274,9532) = 1305884

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FAQs on GCF of Fractions of 3502/274, 2414/9532

1. What is the HCF of 3502,2414?

The HCF of 3502,2414 is 34

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 3502/274, 2414/9532?

Answer: GCF of Numerators as per given numbers 3502/274, 2414/9532 is

GCF of Numerators i.e. for 3502,2414 is 34

LCM of denominators i.e. for 274,9532 is 1305884.

Thus, GCF of Fractions is 34/1305884.Finally, GCF of Fractions for 3502/274, 2414/9532 is 34/1305884.