How to Find GCF of 304/66, 632/1229?

GCF of 304/66, 632/1229

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 304/66, 632/1229 i.e 8/81114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 304/66, 632/1229.

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 304/66,632/1229?

Given fractions are 304/66,632/1229

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 304/66,632/1229, numerators are 304,632

Denominators are 66,1229

The GCF of 304,632 is 8 .

LCM of 66,1229 is 81114.

The greatest common factor of 304/66,632/1229 = [GCF of 304,632]/[LCM of 66,1229]= 8/81114

Therefore, the GCF of 304/66,632/1229 is 8/81114.

Greatest Common Factor of 304,632

To find the highest common factor of 304,632, we have to find the factors of both numbers and list the highest common factor.

The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304

The factors of 632 are 1, 2, 4, 8, 79, 158, 316, 632

The HCF of 304,632 is 8.

Lets's calculate GCF of 304,632

Greatest Common Factor (GCF) of 304,632 By Common Division

2	304, 632
2	152, 316
2	76, 158
	38, 79

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 304,632 By Matching Biggest Common Factor Method

Now, list down the factors of 304

1,2,4,8,16,19,38,76,152,304

Now, list down the factors of 632

1,2,4,8,79,158,316,632

Greatest Common Factor

We found the factors 304,632 . The biggest common factor number is the GCF number.
So the greatest common factor 304,632 is 8.

Lets's calculate LCM of 66,1229

Lowest Common Multiple of 66,1229 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 81114

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/81114

Therefore, the GCF of Fractions 304/66,632/1229 is 8/81114

Least Common Multiple of 66,1229 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 66,1229 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(66,1229) = 1

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

GCF(66,1229) x common factors =1 x 1 = 1

LCM(66,1229) = ( 66 × 1229 ) / 1

LCM(66,1229) = 81114 / 1

LCM(66,1229) = 81114

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 304/66, 632/1229

1. What is the HCF of 304,632?

The HCF of 304,632 is 8

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 304/66, 632/1229?

Answer: GCF of Numerators as per given numbers 304/66, 632/1229 is

GCF of Numerators i.e. for 304,632 is 8

LCM of denominators i.e. for 66,1229 is 81114.

Thus, GCF of Fractions is 8/81114.Finally, GCF of Fractions for 304/66, 632/1229 is 8/81114.