How to Find GCF of 702/342, 3512/7324?

GCF of 702/342, 3512/7324

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 702/342, 3512/7324 i.e 2/1252404 easily. The following is the detailed procedure to determine the greatest common factor of fractions 702/342, 3512/7324.

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 702/342,3512/7324?

Given fractions are 702/342,3512/7324

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 702/342,3512/7324, numerators are 702,3512

Denominators are 342,7324

The GCF of 702,3512 is 2 .

LCM of 342,7324 is 1252404.

The greatest common factor of 702/342,3512/7324 = [GCF of 702,3512]/[LCM of 342,7324]= 2/1252404

Therefore, the GCF of 702/342,3512/7324 is 2/1252404.

Greatest Common Factor of 702,3512

To find the highest common factor of 702,3512, we have to find the factors of both numbers and list the highest common factor.

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702

The factors of 3512 are 1, 2, 4, 8, 439, 878, 1756, 3512

The HCF of 702,3512 is 2.

Lets's calculate GCF of 702,3512

Greatest Common Factor (GCF) of 702,3512 By Common Division

2	702, 3512
	351, 1756

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

Greatest Common Factor of 702,3512 By Matching Biggest Common Factor Method

Now, list down the factors of 702

1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702

Now, list down the factors of 3512

1,2,4,8,439,878,1756,3512

Greatest Common Factor

We found the factors 702,3512 . The biggest common factor number is the GCF number.
So the greatest common factor 702,3512 is 2.

Lets's calculate LCM of 342,7324

Lowest Common Multiple of 342,7324 using Common Division

2	342, 7324
	171, 3662

∴ So the LCM of the given numbers is 2 x 171 x 3662 = 1252404

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1252404

Therefore, the GCF of Fractions 702/342,3512/7324 is 2/1252404

Least Common Multiple of 342,7324 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 342,7324 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(342,7324) = 2

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

GCF(342,7324) x common factors =2 x 1 = 2

LCM(342,7324) = ( 342 × 7324 ) / 2

LCM(342,7324) = 2504808 / 2

LCM(342,7324) = 1252404

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FAQs on GCF of Fractions of 702/342, 3512/7324

1. What is the HCF of 702,3512?

The HCF of 702,3512 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 702/342, 3512/7324?

Answer: GCF of Numerators as per given numbers 702/342, 3512/7324 is

GCF of Numerators i.e. for 702,3512 is 2

LCM of denominators i.e. for 342,7324 is 1252404.

Thus, GCF of Fractions is 2/1252404.Finally, GCF of Fractions for 702/342, 3512/7324 is 2/1252404.