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GCF of 679/40, 512/684

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 679/40, 512/684 i.e 1/6840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 679/40, 512/684.

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 679/40,512/684?

Given fractions are 679/40,512/684

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 679/40,512/684, numerators are 679,512

Denominators are 40,684

The GCF of 679,512 is 1 .

LCM of 40,684 is 6840.

The greatest common factor of 679/40,512/684 = [GCF of 679,512]/[LCM of 40,684]= 1/6840

Therefore, the GCF of 679/40,512/684 is 1/6840.

Greatest Common Factor of 679,512

To find the highest common factor of 679,512, we have to find the factors of both numbers and list the highest common factor.

The factors of 679 are 1, 7, 97, 679

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The HCF of 679,512 is 1.

Lets's calculate GCF of 679,512

Greatest Common Factor (GCF) of 679,512 By Common Division

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

Greatest Common Factor of 679,512 By Matching Biggest Common Factor Method

Greatest Common Factor of 679,512 By Matching Biggest Common Factor Method

Now, list down the factors of 679

:

1,7,97,679

Now, list down the factors of 512

:

1,2,4,8,16,32,64,128,256,512

Greatest Common Factor

We found the factors 679,512 . The biggest common factor number is the GCF number.
So the greatest common factor 679,512 is 1.

Lets's calculate LCM of 40,684

Lowest Common Multiple of 40,684 using Common Division

2 40, 684
2 20, 342
10, 171

∴ So the LCM of the given numbers is 2 x 2 x 10 x 171 = 6840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6840

Therefore, the GCF of Fractions 679/40,512/684 is 1/6840

Least Common Multiple of 40,684 with GCF Formula

Least Common Multiple of 40,684 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 40,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,684) = 4

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

GCF(40,684) x common factors =4 x 1 = 4

LCM(40,684) = ( 40 × 684 ) / 4

LCM(40,684) = 27360 / 4

LCM(40,684) = 6840


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FAQs on GCF of Fractions of 679/40, 512/684

1. What is the HCF of 679,512?

The HCF of 679,512 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 679/40, 512/684?

Answer: GCF of Numerators as per given numbers 679/40, 512/684 is

GCF of Numerators i.e. for 679,512 is 1

LCM of denominators i.e. for 40,684 is 6840.

Thus, GCF of Fractions is 1/6840.Finally, GCF of Fractions for 679/40, 512/684 is 1/6840.