How to Find GCF of 234/267, 510/194?

GCF of 234/267, 510/194

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 234/267, 510/194 i.e 6/51798 easily. The following is the detailed procedure to determine the greatest common factor of fractions 234/267, 510/194.

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 234/267,510/194?

Given fractions are 234/267,510/194

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 234/267,510/194, numerators are 234,510

Denominators are 267,194

The GCF of 234,510 is 6 .

LCM of 267,194 is 51798.

The greatest common factor of 234/267,510/194 = [GCF of 234,510]/[LCM of 267,194]= 6/51798

Therefore, the GCF of 234/267,510/194 is 6/51798.

Greatest Common Factor of 234,510

To find the highest common factor of 234,510, we have to find the factors of both numbers and list the highest common factor.

The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

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

The HCF of 234,510 is 6.

Lets's calculate GCF of 234,510

Greatest Common Factor (GCF) of 234,510 By Common Division

2	234, 510
3	117, 255
	39, 85

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 234,510 By Matching Biggest Common Factor Method

Now, list down the factors of 234

1,2,3,6,9,13,18,26,39,78,117,234

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 234,510 . The biggest common factor number is the GCF number.
So the greatest common factor 234,510 is 6.

Lets's calculate LCM of 267,194

Lowest Common Multiple of 267,194 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 51798

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/51798

Therefore, the GCF of Fractions 234/267,510/194 is 6/51798

Least Common Multiple of 267,194 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 267,194 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(267,194) = 1

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

GCF(267,194) x common factors =1 x 1 = 1

LCM(267,194) = ( 267 × 194 ) / 1

LCM(267,194) = 51798 / 1

LCM(267,194) = 51798

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FAQs on GCF of Fractions of 234/267, 510/194

1. What is the HCF of 234,510?

The HCF of 234,510 is 6

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 234/267, 510/194?

Answer: GCF of Numerators as per given numbers 234/267, 510/194 is

GCF of Numerators i.e. for 234,510 is 6

LCM of denominators i.e. for 267,194 is 51798.

Thus, GCF of Fractions is 6/51798.Finally, GCF of Fractions for 234/267, 510/194 is 6/51798.