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GCF of 698/51, 256/280

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 698/51, 256/280 i.e 2/14280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 698/51, 256/280.

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 698/51,256/280?

Given fractions are 698/51,256/280

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 698/51,256/280, numerators are 698,256

Denominators are 51,280

The GCF of 698,256 is 2 .

LCM of 51,280 is 14280.

The greatest common factor of 698/51,256/280 = [GCF of 698,256]/[LCM of 51,280]= 2/14280

Therefore, the GCF of 698/51,256/280 is 2/14280.

Greatest Common Factor of 698,256

To find the highest common factor of 698,256, we have to find the factors of both numbers and list the highest common factor.

The factors of 698 are 1, 2, 349, 698

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

The HCF of 698,256 is 2.

Lets's calculate GCF of 698,256

Greatest Common Factor (GCF) of 698,256 By Common Division

2 698, 256
349, 128

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

Greatest Common Factor of 698,256 By Matching Biggest Common Factor Method

Greatest Common Factor of 698,256 By Matching Biggest Common Factor Method

Now, list down the factors of 698

:

1,2,349,698

Now, list down the factors of 256

:

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

Greatest Common Factor

We found the factors 698,256 . The biggest common factor number is the GCF number.
So the greatest common factor 698,256 is 2.

Lets's calculate LCM of 51,280

Lowest Common Multiple of 51,280 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 14280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14280

Therefore, the GCF of Fractions 698/51,256/280 is 2/14280

Least Common Multiple of 51,280 with GCF Formula

Least Common Multiple of 51,280 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 51,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(51,280) = 1

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

GCF(51,280) x common factors =1 x 1 = 1

LCM(51,280) = ( 51 × 280 ) / 1

LCM(51,280) = 14280 / 1

LCM(51,280) = 14280


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FAQs on GCF of Fractions of 698/51, 256/280

1. What is the HCF of 698,256?

The HCF of 698,256 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 698/51, 256/280?

Answer: GCF of Numerators as per given numbers 698/51, 256/280 is

GCF of Numerators i.e. for 698,256 is 2

LCM of denominators i.e. for 51,280 is 14280.

Thus, GCF of Fractions is 2/14280.Finally, GCF of Fractions for 698/51, 256/280 is 2/14280.