How to Find GCF of 407/688, 5685/2708?

GCF of 407/688, 5685/2708

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 407/688, 5685/2708 i.e 1/465776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 407/688, 5685/2708.

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 407/688,5685/2708?

Given fractions are 407/688,5685/2708

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 407/688,5685/2708, numerators are 407,5685

Denominators are 688,2708

The GCF of 407,5685 is 1 .

LCM of 688,2708 is 465776.

The greatest common factor of 407/688,5685/2708 = [GCF of 407,5685]/[LCM of 688,2708]= 1/465776

Therefore, the GCF of 407/688,5685/2708 is 1/465776.

Greatest Common Factor of 407,5685

To find the highest common factor of 407,5685, we have to find the factors of both numbers and list the highest common factor.

The factors of 407 are 1, 11, 37, 407

The factors of 5685 are 1, 3, 5, 15, 379, 1137, 1895, 5685

The HCF of 407,5685 is 1.

Lets's calculate GCF of 407,5685

Greatest Common Factor (GCF) of 407,5685 By Common Division

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

Greatest Common Factor of 407,5685 By Matching Biggest Common Factor Method

Now, list down the factors of 407

1,11,37,407

Now, list down the factors of 5685

1,3,5,15,379,1137,1895,5685

Greatest Common Factor

We found the factors 407,5685 . The biggest common factor number is the GCF number.
So the greatest common factor 407,5685 is 1.

Lets's calculate LCM of 688,2708

Lowest Common Multiple of 688,2708 using Common Division

2	688, 2708
2	344, 1354
	172, 677

∴ So the LCM of the given numbers is 2 x 2 x 172 x 677 = 465776

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/465776

Therefore, the GCF of Fractions 407/688,5685/2708 is 1/465776

Least Common Multiple of 688,2708 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 688,2708 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(688,2708) = 4

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

GCF(688,2708) x common factors =4 x 1 = 4

LCM(688,2708) = ( 688 × 2708 ) / 4

LCM(688,2708) = 1863104 / 4

LCM(688,2708) = 465776

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FAQs on GCF of Fractions of 407/688, 5685/2708

1. What is the HCF of 407,5685?

The HCF of 407,5685 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 407/688, 5685/2708?

Answer: GCF of Numerators as per given numbers 407/688, 5685/2708 is

GCF of Numerators i.e. for 407,5685 is 1

LCM of denominators i.e. for 688,2708 is 465776.

Thus, GCF of Fractions is 1/465776.Finally, GCF of Fractions for 407/688, 5685/2708 is 1/465776.