How to Find GCF of 123/78, 510/7801?

GCF of 123/78, 510/7801

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 123/78, 510/7801 i.e 3/608478 easily. The following is the detailed procedure to determine the greatest common factor of fractions 123/78, 510/7801.

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 123/78,510/7801?

Given fractions are 123/78,510/7801

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 123/78,510/7801, numerators are 123,510

Denominators are 78,7801

The GCF of 123,510 is 3 .

LCM of 78,7801 is 608478.

The greatest common factor of 123/78,510/7801 = [GCF of 123,510]/[LCM of 78,7801]= 3/608478

Therefore, the GCF of 123/78,510/7801 is 3/608478.

Greatest Common Factor of 123,510

To find the highest common factor of 123,510, we have to find the factors of both numbers and list the highest common factor.

The factors of 123 are 1, 3, 41, 123

The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510

The HCF of 123,510 is 3.

Lets's calculate GCF of 123,510

Greatest Common Factor (GCF) of 123,510 By Common Division

3	123, 510
	41, 170

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 123,510 By Matching Biggest Common Factor Method

Now, list down the factors of 123

1,3,41,123

Now, list down the factors of 510

1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510

Greatest Common Factor

We found the factors 123,510 . The biggest common factor number is the GCF number.
So the greatest common factor 123,510 is 3.

Lets's calculate LCM of 78,7801

Lowest Common Multiple of 78,7801 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 608478

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/608478

Therefore, the GCF of Fractions 123/78,510/7801 is 3/608478

Least Common Multiple of 78,7801 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 78,7801 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,7801) = 1

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

GCF(78,7801) x common factors =1 x 1 = 1

LCM(78,7801) = ( 78 × 7801 ) / 1

LCM(78,7801) = 608478 / 1

LCM(78,7801) = 608478

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FAQs on GCF of Fractions of 123/78, 510/7801

1. What is the HCF of 123,510?

The HCF of 123,510 is 3

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 123/78, 510/7801?

Answer: GCF of Numerators as per given numbers 123/78, 510/7801 is

GCF of Numerators i.e. for 123,510 is 3

LCM of denominators i.e. for 78,7801 is 608478.

Thus, GCF of Fractions is 3/608478.Finally, GCF of Fractions for 123/78, 510/7801 is 3/608478.