How to Find GCF of 780/59, 130/223?

GCF of 780/59, 130/223

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 780/59, 130/223 i.e 130/13157 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/59, 130/223.

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 780/59,130/223?

Given fractions are 780/59,130/223

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 780/59,130/223, numerators are 780,130

Denominators are 59,223

The GCF of 780,130 is 130 .

LCM of 59,223 is 13157.

The greatest common factor of 780/59,130/223 = [GCF of 780,130]/[LCM of 59,223]= 130/13157

Therefore, the GCF of 780/59,130/223 is 130/13157.

Greatest Common Factor of 780,130

To find the highest common factor of 780,130, we have to find the factors of both numbers and list the highest common factor.

The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780

The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130

The HCF of 780,130 is 130.

Lets's calculate GCF of 780,130

Greatest Common Factor (GCF) of 780,130 By Common Division

2	780, 130
5	390, 65
13	78, 13
	6, 1

∴ So the GCF of the given numbers is 2 x 5 x 13 = 130

Greatest Common Factor of 780,130 By Matching Biggest Common Factor Method

Now, list down the factors of 780

1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780

Now, list down the factors of 130

1,2,5,10,13,26,65,130

Greatest Common Factor

We found the factors 780,130 . The biggest common factor number is the GCF number.
So the greatest common factor 780,130 is 130.

Lets's calculate LCM of 59,223

Lowest Common Multiple of 59,223 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 13157

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 130/13157

Therefore, the GCF of Fractions 780/59,130/223 is 130/13157

Least Common Multiple of 59,223 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 59,223 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(59,223) = 1

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

GCF(59,223) x common factors =1 x 1 = 1

LCM(59,223) = ( 59 × 223 ) / 1

LCM(59,223) = 13157 / 1

LCM(59,223) = 13157

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FAQs on GCF of Fractions of 780/59, 130/223

1. What is the HCF of 780,130?

The HCF of 780,130 is 130

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 780/59, 130/223?

Answer: GCF of Numerators as per given numbers 780/59, 130/223 is

GCF of Numerators i.e. for 780,130 is 130

LCM of denominators i.e. for 59,223 is 13157.

Thus, GCF of Fractions is 130/13157.Finally, GCF of Fractions for 780/59, 130/223 is 130/13157.