How to Find GCF of 274/980, 440/656?

GCF of 274/980, 440/656

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 274/980, 440/656 i.e 2/160720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 274/980, 440/656.

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 274/980,440/656?

Given fractions are 274/980,440/656

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 274/980,440/656, numerators are 274,440

Denominators are 980,656

The GCF of 274,440 is 2 .

LCM of 980,656 is 160720.

The greatest common factor of 274/980,440/656 = [GCF of 274,440]/[LCM of 980,656]= 2/160720

Therefore, the GCF of 274/980,440/656 is 2/160720.

Greatest Common Factor of 274,440

To find the highest common factor of 274,440, we have to find the factors of both numbers and list the highest common factor.

The factors of 274 are 1, 2, 137, 274

The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440

The HCF of 274,440 is 2.

Lets's calculate GCF of 274,440

Greatest Common Factor (GCF) of 274,440 By Common Division

2	274, 440
	137, 220

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

Greatest Common Factor of 274,440 By Matching Biggest Common Factor Method

Now, list down the factors of 274

1,2,137,274

Now, list down the factors of 440

1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440

Greatest Common Factor

We found the factors 274,440 . The biggest common factor number is the GCF number.
So the greatest common factor 274,440 is 2.

Lets's calculate LCM of 980,656

Lowest Common Multiple of 980,656 using Common Division

2	980, 656
2	490, 328
	245, 164

∴ So the LCM of the given numbers is 2 x 2 x 245 x 164 = 160720

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/160720

Therefore, the GCF of Fractions 274/980,440/656 is 2/160720

Least Common Multiple of 980,656 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 980,656 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(980,656) = 4

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

GCF(980,656) x common factors =4 x 1 = 4

LCM(980,656) = ( 980 × 656 ) / 4

LCM(980,656) = 642880 / 4

LCM(980,656) = 160720

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FAQs on GCF of Fractions of 274/980, 440/656

1. What is the HCF of 274,440?

The HCF of 274,440 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 274/980, 440/656?

Answer: GCF of Numerators as per given numbers 274/980, 440/656 is

GCF of Numerators i.e. for 274,440 is 2

LCM of denominators i.e. for 980,656 is 160720.

Thus, GCF of Fractions is 2/160720.Finally, GCF of Fractions for 274/980, 440/656 is 2/160720.