How to Find GCF of 214/428, 980/400?

GCF of 214/428, 980/400

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 214/428, 980/400 i.e 2/42800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 214/428, 980/400.

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 214/428,980/400?

Given fractions are 214/428,980/400

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 214/428,980/400, numerators are 214,980

Denominators are 428,400

The GCF of 214,980 is 2 .

LCM of 428,400 is 42800.

The greatest common factor of 214/428,980/400 = [GCF of 214,980]/[LCM of 428,400]= 2/42800

Therefore, the GCF of 214/428,980/400 is 2/42800.

Greatest Common Factor of 214,980

To find the highest common factor of 214,980, we have to find the factors of both numbers and list the highest common factor.

The factors of 214 are 1, 2, 107, 214

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980

The HCF of 214,980 is 2.

Lets's calculate GCF of 214,980

Greatest Common Factor (GCF) of 214,980 By Common Division

2	214, 980
	107, 490

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

Greatest Common Factor of 214,980 By Matching Biggest Common Factor Method

Now, list down the factors of 214

1,2,107,214

Now, list down the factors of 980

1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980

Greatest Common Factor

We found the factors 214,980 . The biggest common factor number is the GCF number.
So the greatest common factor 214,980 is 2.

Lets's calculate LCM of 428,400

Lowest Common Multiple of 428,400 using Common Division

2	428, 400
2	214, 200
	107, 100

∴ So the LCM of the given numbers is 2 x 2 x 107 x 100 = 42800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/42800

Therefore, the GCF of Fractions 214/428,980/400 is 2/42800

Least Common Multiple of 428,400 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 428,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(428,400) = 4

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

GCF(428,400) x common factors =4 x 1 = 4

LCM(428,400) = ( 428 × 400 ) / 4

LCM(428,400) = 171200 / 4

LCM(428,400) = 42800

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FAQs on GCF of Fractions of 214/428, 980/400

1. What is the HCF of 214,980?

The HCF of 214,980 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 214/428, 980/400?

Answer: GCF of Numerators as per given numbers 214/428, 980/400 is

GCF of Numerators i.e. for 214,980 is 2

LCM of denominators i.e. for 428,400 is 42800.

Thus, GCF of Fractions is 2/42800.Finally, GCF of Fractions for 214/428, 980/400 is 2/42800.