How to Find GCF of 31/684, 3007/2048?

GCF of 31/684, 3007/2048

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 31/684, 3007/2048 i.e 31/350208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/684, 3007/2048.

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 31/684,3007/2048?

Given fractions are 31/684,3007/2048

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 31/684,3007/2048, numerators are 31,3007

Denominators are 684,2048

The GCF of 31,3007 is 31 .

LCM of 684,2048 is 350208.

The greatest common factor of 31/684,3007/2048 = [GCF of 31,3007]/[LCM of 684,2048]= 31/350208

Therefore, the GCF of 31/684,3007/2048 is 31/350208.

Greatest Common Factor of 31,3007

To find the highest common factor of 31,3007, we have to find the factors of both numbers and list the highest common factor.

The factors of 31 are 1, 31

The factors of 3007 are 1, 31, 97, 3007

The HCF of 31,3007 is 31.

Lets's calculate GCF of 31,3007

Greatest Common Factor (GCF) of 31,3007 By Common Division

31	31, 3007
	1, 97

∴ So the GCF of the given numbers is 31 = 31

Greatest Common Factor of 31,3007 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 3007

1,31,97,3007

Greatest Common Factor

We found the factors 31,3007 . The biggest common factor number is the GCF number.
So the greatest common factor 31,3007 is 31.

Lets's calculate LCM of 684,2048

Lowest Common Multiple of 684,2048 using Common Division

2	684, 2048
2	342, 1024
	171, 512

∴ So the LCM of the given numbers is 2 x 2 x 171 x 512 = 350208

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/350208

Therefore, the GCF of Fractions 31/684,3007/2048 is 31/350208

Least Common Multiple of 684,2048 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 684,2048 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(684,2048) = 4

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

GCF(684,2048) x common factors =4 x 1 = 4

LCM(684,2048) = ( 684 × 2048 ) / 4

LCM(684,2048) = 1400832 / 4

LCM(684,2048) = 350208

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FAQs on GCF of Fractions of 31/684, 3007/2048

1. What is the HCF of 31,3007?

The HCF of 31,3007 is 31

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 31/684, 3007/2048?

Answer: GCF of Numerators as per given numbers 31/684, 3007/2048 is

GCF of Numerators i.e. for 31,3007 is 31

LCM of denominators i.e. for 684,2048 is 350208.

Thus, GCF of Fractions is 31/350208.Finally, GCF of Fractions for 31/684, 3007/2048 is 31/350208.