How to Find GCF of 708/666, 5314/3708?

GCF of 708/666, 5314/3708

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 708/666, 5314/3708 i.e 2/137196 easily. The following is the detailed procedure to determine the greatest common factor of fractions 708/666, 5314/3708.

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 708/666,5314/3708?

Given fractions are 708/666,5314/3708

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 708/666,5314/3708, numerators are 708,5314

Denominators are 666,3708

The GCF of 708,5314 is 2 .

LCM of 666,3708 is 137196.

The greatest common factor of 708/666,5314/3708 = [GCF of 708,5314]/[LCM of 666,3708]= 2/137196

Therefore, the GCF of 708/666,5314/3708 is 2/137196.

Greatest Common Factor of 708,5314

To find the highest common factor of 708,5314, we have to find the factors of both numbers and list the highest common factor.

The factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708

The factors of 5314 are 1, 2, 2657, 5314

The HCF of 708,5314 is 2.

Lets's calculate GCF of 708,5314

Greatest Common Factor (GCF) of 708,5314 By Common Division

2	708, 5314
	354, 2657

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

Greatest Common Factor of 708,5314 By Matching Biggest Common Factor Method

Now, list down the factors of 708

1,2,3,4,6,12,59,118,177,236,354,708

Now, list down the factors of 5314

1,2,2657,5314

Greatest Common Factor

We found the factors 708,5314 . The biggest common factor number is the GCF number.
So the greatest common factor 708,5314 is 2.

Lets's calculate LCM of 666,3708

Lowest Common Multiple of 666,3708 using Common Division

2	666, 3708
3	333, 1854
3	111, 618
	37, 206

∴ So the LCM of the given numbers is 2 x 3 x 3 x 37 x 206 = 137196

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/137196

Therefore, the GCF of Fractions 708/666,5314/3708 is 2/137196

Least Common Multiple of 666,3708 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 666,3708 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(666,3708) = 18

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

GCF(666,3708) x common factors =18 x 1 = 18

LCM(666,3708) = ( 666 × 3708 ) / 18

LCM(666,3708) = 2469528 / 18

LCM(666,3708) = 137196

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FAQs on GCF of Fractions of 708/666, 5314/3708

1. What is the HCF of 708,5314?

The HCF of 708,5314 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 708/666, 5314/3708?

Answer: GCF of Numerators as per given numbers 708/666, 5314/3708 is

GCF of Numerators i.e. for 708,5314 is 2

LCM of denominators i.e. for 666,3708 is 137196.

Thus, GCF of Fractions is 2/137196.Finally, GCF of Fractions for 708/666, 5314/3708 is 2/137196.