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GCF of 458/144, 375/168

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 458/144, 375/168 i.e 1/1008 easily. The following is the detailed procedure to determine the greatest common factor of fractions 458/144, 375/168.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 458/144,375/168?

Given fractions are 458/144,375/168

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 458/144,375/168, numerators are 458,375

Denominators are 144,168

The GCF of 458,375 is 1 .

LCM of 144,168 is 1008.

The greatest common factor of 458/144,375/168 = [GCF of 458,375]/[LCM of 144,168]= 1/1008

Therefore, the GCF of 458/144,375/168 is 1/1008.

Greatest Common Factor of 458,375

To find the highest common factor of 458,375, we have to find the factors of both numbers and list the highest common factor.

The factors of 458 are 1, 2, 229, 458

The factors of 375 are 1, 3, 5, 15, 25, 75, 125, 375

The HCF of 458,375 is 1.

Lets's calculate GCF of 458,375

Greatest Common Factor (GCF) of 458,375 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 458,375 By Matching Biggest Common Factor Method

Greatest Common Factor of 458,375 By Matching Biggest Common Factor Method

Now, list down the factors of 458

:

1,2,229,458

Now, list down the factors of 375

:

1,3,5,15,25,75,125,375

Greatest Common Factor

We found the factors 458,375 . The biggest common factor number is the GCF number.
So the greatest common factor 458,375 is 1.

Lets's calculate LCM of 144,168

Lowest Common Multiple of 144,168 using Common Division

2 144, 168
2 72, 84
2 36, 42
3 18, 21
6, 7

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 6 x 7 = 1008

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1008

Therefore, the GCF of Fractions 458/144,375/168 is 1/1008

Least Common Multiple of 144,168 with GCF Formula

Least Common Multiple of 144,168 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 144,168 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(144,168) = 24

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

GCF(144,168) x common factors =24 x 1 = 24

LCM(144,168) = ( 144 × 168 ) / 24

LCM(144,168) = 24192 / 24

LCM(144,168) = 1008


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FAQs on GCF of Fractions of 458/144, 375/168

1. What is the HCF of 458,375?

The HCF of 458,375 is 1

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 458/144, 375/168?

Answer: GCF of Numerators as per given numbers 458/144, 375/168 is

GCF of Numerators i.e. for 458,375 is 1

LCM of denominators i.e. for 144,168 is 1008.

Thus, GCF of Fractions is 1/1008.Finally, GCF of Fractions for 458/144, 375/168 is 1/1008.