How to Find GCF of 748/41, 680/679?

GCF of 748/41, 680/679

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 748/41, 680/679 i.e 68/27839 easily. The following is the detailed procedure to determine the greatest common factor of fractions 748/41, 680/679.

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 748/41,680/679?

Given fractions are 748/41,680/679

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 748/41,680/679, numerators are 748,680

Denominators are 41,679

The GCF of 748,680 is 68 .

LCM of 41,679 is 27839.

The greatest common factor of 748/41,680/679 = [GCF of 748,680]/[LCM of 41,679]= 68/27839

Therefore, the GCF of 748/41,680/679 is 68/27839.

Greatest Common Factor of 748,680

To find the highest common factor of 748,680, we have to find the factors of both numbers and list the highest common factor.

The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680

The HCF of 748,680 is 68.

Lets's calculate GCF of 748,680

Greatest Common Factor (GCF) of 748,680 By Common Division

2	748, 680
2	374, 340
17	187, 170
	11, 10

∴ So the GCF of the given numbers is 2 x 2 x 17 = 68

Greatest Common Factor of 748,680 By Matching Biggest Common Factor Method

Now, list down the factors of 748

1,2,4,11,17,22,34,44,68,187,374,748

Now, list down the factors of 680

1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680

Greatest Common Factor

We found the factors 748,680 . The biggest common factor number is the GCF number.
So the greatest common factor 748,680 is 68.

Lets's calculate LCM of 41,679

Lowest Common Multiple of 41,679 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 27839

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 68/27839

Therefore, the GCF of Fractions 748/41,680/679 is 68/27839

Least Common Multiple of 41,679 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 41,679 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(41,679) = 1

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

GCF(41,679) x common factors =1 x 1 = 1

LCM(41,679) = ( 41 × 679 ) / 1

LCM(41,679) = 27839 / 1

LCM(41,679) = 27839

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FAQs on GCF of Fractions of 748/41, 680/679

1. What is the HCF of 748,680?

The HCF of 748,680 is 68

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 748/41, 680/679?

Answer: GCF of Numerators as per given numbers 748/41, 680/679 is

GCF of Numerators i.e. for 748,680 is 68

LCM of denominators i.e. for 41,679 is 27839.

Thus, GCF of Fractions is 68/27839.Finally, GCF of Fractions for 748/41, 680/679 is 68/27839.