How to Find GCF of 2/58, 109/12, 688/49?

GCF of 2/58, 109/12, 688/49

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 2/58, 109/12, 688/49 i.e 1/17052 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2/58, 109/12, 688/49.

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 2/58,109/12,688/49?

Given fractions are 2/58,109/12,688/49

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 2/58,109/12,688/49, numerators are 2,109,688

Denominators are 58,12,49

The GCF of 2,109,688 is 1 .

LCM of 58,12,49 is 17052.

The greatest common factor of 2/58,109/12,688/49 = [GCF of 2,109,688]/[LCM of 58,12,49]= 1/17052

Therefore, the GCF of 2/58,109/12,688/49 is 1/17052.

Greatest Common Factor of 2,109,688

To find the highest common factor of 2,109,688, we have to find the factors of both numbers and list the highest common factor.

The factors of 2 are 1, 2

The factors of 109 are 1, 109

The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688

The HCF of 2,109,688 is 1.

Lets's calculate GCF of 2,109,688

Greatest Common Factor (GCF) of 2,109,688 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 2,109,688 By Matching Biggest Common Factor Method

Now, list down the factors of 2

1,2

Now, list down the factors of 109

1,109

Now, list down the factors of 688

1,2,4,8,16,43,86,172,344,688

Greatest Common Factor

We found the factors 2,109,688 . The biggest common factor number is the GCF number.
So the greatest common factor 2,109,688 is 1.

Lets's calculate LCM of 58,12,49

Lowest Common Multiple of 58,12,49 using Common Division

2	58, 12, 49
	29, 6, 49

∴ So the LCM of the given numbers is 2 x 29 x 6 x 49 = 17052

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17052

Therefore, the GCF of Fractions 2/58,109/12,688/49 is 1/17052

Least Common Multiple of 58,12,49 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 58,12,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(58,12,49) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(58,12,49) x common factors =1 x 2 = 2

LCM(58,12,49) = ( 58 × 12 × 49 ) / 2

LCM(58,12,49) = 34104 / 2

LCM(58,12,49) = 17052

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FAQs on GCF of Fractions of 2/58, 109/12, 688/49

1. What is the HCF of 2,109,688?

The HCF of 2,109,688 is 1

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 2/58, 109/12, 688/49?

Answer: GCF of Numerators as per given numbers 2/58, 109/12, 688/49 is

GCF of Numerators i.e. for 2,109,688 is 1

LCM of denominators i.e. for 58,12,49 is 17052.

Thus, GCF of Fractions is 1/17052.Finally, GCF of Fractions for 2/58, 109/12, 688/49 is 1/17052.