How to Find GCF of 456/233, 3144/666?

GCF of 456/233, 3144/666

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 456/233, 3144/666 i.e 24/155178 easily. The following is the detailed procedure to determine the greatest common factor of fractions 456/233, 3144/666.

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 456/233,3144/666?

Given fractions are 456/233,3144/666

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 456/233,3144/666, numerators are 456,3144

Denominators are 233,666

The GCF of 456,3144 is 24 .

LCM of 233,666 is 155178.

The greatest common factor of 456/233,3144/666 = [GCF of 456,3144]/[LCM of 233,666]= 24/155178

Therefore, the GCF of 456/233,3144/666 is 24/155178.

Greatest Common Factor of 456,3144

To find the highest common factor of 456,3144, we have to find the factors of both numbers and list the highest common factor.

The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456

The factors of 3144 are 1, 2, 3, 4, 6, 8, 12, 24, 131, 262, 393, 524, 786, 1048, 1572, 3144

The HCF of 456,3144 is 24.

Lets's calculate GCF of 456,3144

Greatest Common Factor (GCF) of 456,3144 By Common Division

2	456, 3144
2	228, 1572
2	114, 786
3	57, 393
	19, 131

∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24

Greatest Common Factor of 456,3144 By Matching Biggest Common Factor Method

Now, list down the factors of 456

1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456

Now, list down the factors of 3144

1,2,3,4,6,8,12,24,131,262,393,524,786,1048,1572,3144

Greatest Common Factor

We found the factors 456,3144 . The biggest common factor number is the GCF number.
So the greatest common factor 456,3144 is 24.

Lets's calculate LCM of 233,666

Lowest Common Multiple of 233,666 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 155178

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/155178

Therefore, the GCF of Fractions 456/233,3144/666 is 24/155178

Least Common Multiple of 233,666 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 233,666 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(233,666) = 1

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

GCF(233,666) x common factors =1 x 1 = 1

LCM(233,666) = ( 233 × 666 ) / 1

LCM(233,666) = 155178 / 1

LCM(233,666) = 155178

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FAQs on GCF of Fractions of 456/233, 3144/666

1. What is the HCF of 456,3144?

The HCF of 456,3144 is 24

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 456/233, 3144/666?

Answer: GCF of Numerators as per given numbers 456/233, 3144/666 is

GCF of Numerators i.e. for 456,3144 is 24

LCM of denominators i.e. for 233,666 is 155178.

Thus, GCF of Fractions is 24/155178.Finally, GCF of Fractions for 456/233, 3144/666 is 24/155178.