How to Find GCF of 2130/280, 1988/627?

GCF of 2130/280, 1988/627

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 2130/280, 1988/627 i.e 142/175560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2130/280, 1988/627.

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 2130/280,1988/627?

Given fractions are 2130/280,1988/627

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 2130/280,1988/627, numerators are 2130,1988

Denominators are 280,627

The GCF of 2130,1988 is 142 .

LCM of 280,627 is 175560.

The greatest common factor of 2130/280,1988/627 = [GCF of 2130,1988]/[LCM of 280,627]= 142/175560

Therefore, the GCF of 2130/280,1988/627 is 142/175560.

Greatest Common Factor of 2130,1988

To find the highest common factor of 2130,1988, we have to find the factors of both numbers and list the highest common factor.

The factors of 2130 are 1, 2, 3, 5, 6, 10, 15, 30, 71, 142, 213, 355, 426, 710, 1065, 2130

The factors of 1988 are 1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, 1988

The HCF of 2130,1988 is 142.

Lets's calculate GCF of 2130,1988

Greatest Common Factor (GCF) of 2130,1988 By Common Division

2	2130, 1988
71	1065, 994
	15, 14

∴ So the GCF of the given numbers is 2 x 71 = 142

Greatest Common Factor of 2130,1988 By Matching Biggest Common Factor Method

Now, list down the factors of 2130

1,2,3,5,6,10,15,30,71,142,213,355,426,710,1065,2130

Now, list down the factors of 1988

1,2,4,7,14,28,71,142,284,497,994,1988

Greatest Common Factor

We found the factors 2130,1988 . The biggest common factor number is the GCF number.
So the greatest common factor 2130,1988 is 142.

Lets's calculate LCM of 280,627

Lowest Common Multiple of 280,627 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 175560

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 142/175560

Therefore, the GCF of Fractions 2130/280,1988/627 is 142/175560

Least Common Multiple of 280,627 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 280,627 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(280,627) = 1

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

GCF(280,627) x common factors =1 x 1 = 1

LCM(280,627) = ( 280 × 627 ) / 1

LCM(280,627) = 175560 / 1

LCM(280,627) = 175560

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FAQs on GCF of Fractions of 2130/280, 1988/627

1. What is the HCF of 2130,1988?

The HCF of 2130,1988 is 142

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 2130/280, 1988/627?

Answer: GCF of Numerators as per given numbers 2130/280, 1988/627 is

GCF of Numerators i.e. for 2130,1988 is 142

LCM of denominators i.e. for 280,627 is 175560.

Thus, GCF of Fractions is 142/175560.Finally, GCF of Fractions for 2130/280, 1988/627 is 142/175560.