How to Find GCF of 682/824, 2120/256?

GCF of 682/824, 2120/256

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 682/824, 2120/256 i.e 2/26368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 682/824, 2120/256.

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 682/824,2120/256?

Given fractions are 682/824,2120/256

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 682/824,2120/256, numerators are 682,2120

Denominators are 824,256

The GCF of 682,2120 is 2 .

LCM of 824,256 is 26368.

The greatest common factor of 682/824,2120/256 = [GCF of 682,2120]/[LCM of 824,256]= 2/26368

Therefore, the GCF of 682/824,2120/256 is 2/26368.

Greatest Common Factor of 682,2120

To find the highest common factor of 682,2120, we have to find the factors of both numbers and list the highest common factor.

The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682

The factors of 2120 are 1, 2, 4, 5, 8, 10, 20, 40, 53, 106, 212, 265, 424, 530, 1060, 2120

The HCF of 682,2120 is 2.

Lets's calculate GCF of 682,2120

Greatest Common Factor (GCF) of 682,2120 By Common Division

2	682, 2120
	341, 1060

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 682,2120 By Matching Biggest Common Factor Method

Now, list down the factors of 682

1,2,11,22,31,62,341,682

Now, list down the factors of 2120

1,2,4,5,8,10,20,40,53,106,212,265,424,530,1060,2120

Greatest Common Factor

We found the factors 682,2120 . The biggest common factor number is the GCF number.
So the greatest common factor 682,2120 is 2.

Lets's calculate LCM of 824,256

Lowest Common Multiple of 824,256 using Common Division

2	824, 256
2	412, 128
2	206, 64
	103, 32

∴ So the LCM of the given numbers is 2 x 2 x 2 x 103 x 32 = 26368

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/26368

Therefore, the GCF of Fractions 682/824,2120/256 is 2/26368

Least Common Multiple of 824,256 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 824,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(824,256) = 8

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

GCF(824,256) x common factors =8 x 1 = 8

LCM(824,256) = ( 824 × 256 ) / 8

LCM(824,256) = 210944 / 8

LCM(824,256) = 26368

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 682/824, 2120/256

1. What is the HCF of 682,2120?

The HCF of 682,2120 is 2

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 682/824, 2120/256?

Answer: GCF of Numerators as per given numbers 682/824, 2120/256 is

GCF of Numerators i.e. for 682,2120 is 2

LCM of denominators i.e. for 824,256 is 26368.

Thus, GCF of Fractions is 2/26368.Finally, GCF of Fractions for 682/824, 2120/256 is 2/26368.