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GCF of 759/30, 880/709

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 759/30, 880/709 i.e 11/21270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 759/30, 880/709.

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 759/30,880/709?

Given fractions are 759/30,880/709

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 759/30,880/709, numerators are 759,880

Denominators are 30,709

The GCF of 759,880 is 11 .

LCM of 30,709 is 21270.

The greatest common factor of 759/30,880/709 = [GCF of 759,880]/[LCM of 30,709]= 11/21270

Therefore, the GCF of 759/30,880/709 is 11/21270.

Greatest Common Factor of 759,880

To find the highest common factor of 759,880, we have to find the factors of both numbers and list the highest common factor.

The factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759

The factors of 880 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880

The HCF of 759,880 is 11.

Lets's calculate GCF of 759,880

Greatest Common Factor (GCF) of 759,880 By Common Division

11 759, 880
69, 80

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

Greatest Common Factor of 759,880 By Matching Biggest Common Factor Method

Greatest Common Factor of 759,880 By Matching Biggest Common Factor Method

Now, list down the factors of 759

:

1,3,11,23,33,69,253,759

Now, list down the factors of 880

:

1,2,4,5,8,10,11,16,20,22,40,44,55,80,88,110,176,220,440,880

Greatest Common Factor

We found the factors 759,880 . The biggest common factor number is the GCF number.
So the greatest common factor 759,880 is 11.


Lets's calculate LCM of 30,709

Lowest Common Multiple of 30,709 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 21270

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/21270

Therefore, the GCF of Fractions 759/30,880/709 is 11/21270

Least Common Multiple of 30,709 with GCF Formula

Least Common Multiple of 30,709 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 30,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,709) = 1

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

GCF(30,709) x common factors =1 x 1 = 1

LCM(30,709) = ( 30 × 709 ) / 1

LCM(30,709) = 21270 / 1

LCM(30,709) = 21270


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 759/30, 880/709

1. What is the HCF of 759,880?

The HCF of 759,880 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 759/30, 880/709?

Answer: GCF of Numerators as per given numbers 759/30, 880/709 is

GCF of Numerators i.e. for 759,880 is 11

LCM of denominators i.e. for 30,709 is 21270.

Thus, GCF of Fractions is 11/21270.Finally, GCF of Fractions for 759/30, 880/709 is 11/21270.