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GCF of 748/522, 5709/353

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 748/522, 5709/353 i.e 11/184266 easily. The following is the detailed procedure to determine the greatest common factor of fractions 748/522, 5709/353.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 748/522,5709/353?

Given fractions are 748/522,5709/353

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 748/522,5709/353, numerators are 748,5709

Denominators are 522,353

The GCF of 748,5709 is 11 .

LCM of 522,353 is 184266.

The greatest common factor of 748/522,5709/353 = [GCF of 748,5709]/[LCM of 522,353]= 11/184266

Therefore, the GCF of 748/522,5709/353 is 11/184266.

Greatest Common Factor of 748,5709

To find the highest common factor of 748,5709, 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 5709 are 1, 3, 11, 33, 173, 519, 1903, 5709

The HCF of 748,5709 is 11.

Lets's calculate GCF of 748,5709

Greatest Common Factor (GCF) of 748,5709 By Common Division

11 748, 5709
68, 519

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 748,5709 By Matching Biggest Common Factor Method

Greatest Common Factor of 748,5709 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 5709

:

1,3,11,33,173,519,1903,5709

Greatest Common Factor

We found the factors 748,5709 . The biggest common factor number is the GCF number.
So the greatest common factor 748,5709 is 11.


Lets's calculate LCM of 522,353

Lowest Common Multiple of 522,353 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 184266

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/184266

Therefore, the GCF of Fractions 748/522,5709/353 is 11/184266

Least Common Multiple of 522,353 with GCF Formula

Least Common Multiple of 522,353 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 522,353 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(522,353) = 1

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

GCF(522,353) x common factors =1 x 1 = 1

LCM(522,353) = ( 522 × 353 ) / 1

LCM(522,353) = 184266 / 1

LCM(522,353) = 184266


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 748/522, 5709/353

1. What is the HCF of 748,5709?

The HCF of 748,5709 is 11

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 748/522, 5709/353?

Answer: GCF of Numerators as per given numbers 748/522, 5709/353 is

GCF of Numerators i.e. for 748,5709 is 11

LCM of denominators i.e. for 522,353 is 184266.

Thus, GCF of Fractions is 11/184266.Finally, GCF of Fractions for 748/522, 5709/353 is 11/184266.