How to Find GCF of 759/816, 1657/684?

GCF of 759/816, 1657/684

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 759/816, 1657/684 i.e 1/46512 easily. The following is the detailed procedure to determine the greatest common factor of fractions 759/816, 1657/684.

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 759/816,1657/684?

Given fractions are 759/816,1657/684

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 759/816,1657/684, numerators are 759,1657

Denominators are 816,684

The GCF of 759,1657 is 1 .

LCM of 816,684 is 46512.

The greatest common factor of 759/816,1657/684 = [GCF of 759,1657]/[LCM of 816,684]= 1/46512

Therefore, the GCF of 759/816,1657/684 is 1/46512.

Greatest Common Factor of 759,1657

To find the highest common factor of 759,1657, 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 1657 are 1, 1657

The HCF of 759,1657 is 1.

Lets's calculate GCF of 759,1657

Greatest Common Factor (GCF) of 759,1657 By Common Division

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

Greatest Common Factor of 759,1657 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 1657

1,1657

Greatest Common Factor

We found the factors 759,1657 . The biggest common factor number is the GCF number.
So the greatest common factor 759,1657 is 1.

Lets's calculate LCM of 816,684

Lowest Common Multiple of 816,684 using Common Division

2	816, 684
2	408, 342
3	204, 171
	68, 57

∴ So the LCM of the given numbers is 2 x 2 x 3 x 68 x 57 = 46512

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/46512

Therefore, the GCF of Fractions 759/816,1657/684 is 1/46512

Least Common Multiple of 816,684 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 816,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(816,684) = 12

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

GCF(816,684) x common factors =12 x 1 = 12

LCM(816,684) = ( 816 × 684 ) / 12

LCM(816,684) = 558144 / 12

LCM(816,684) = 46512

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FAQs on GCF of Fractions of 759/816, 1657/684

1. What is the HCF of 759,1657?

The HCF of 759,1657 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 759/816, 1657/684?

Answer: GCF of Numerators as per given numbers 759/816, 1657/684 is

GCF of Numerators i.e. for 759,1657 is 1

LCM of denominators i.e. for 816,684 is 46512.

Thus, GCF of Fractions is 1/46512.Finally, GCF of Fractions for 759/816, 1657/684 is 1/46512.