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GCF of 142/224, 278/284

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 142/224, 278/284 i.e 2/15904 easily. The following is the detailed procedure to determine the greatest common factor of fractions 142/224, 278/284.

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 142/224,278/284?

Given fractions are 142/224,278/284

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 142/224,278/284, numerators are 142,278

Denominators are 224,284

The GCF of 142,278 is 2 .

LCM of 224,284 is 15904.

The greatest common factor of 142/224,278/284 = [GCF of 142,278]/[LCM of 224,284]= 2/15904

Therefore, the GCF of 142/224,278/284 is 2/15904.

Greatest Common Factor of 142,278

To find the highest common factor of 142,278, we have to find the factors of both numbers and list the highest common factor.

The factors of 142 are 1, 2, 71, 142

The factors of 278 are 1, 2, 139, 278

The HCF of 142,278 is 2.

Lets's calculate GCF of 142,278

Greatest Common Factor (GCF) of 142,278 By Common Division

2 142, 278
71, 139

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

Greatest Common Factor of 142,278 By Matching Biggest Common Factor Method

Greatest Common Factor of 142,278 By Matching Biggest Common Factor Method

Now, list down the factors of 142

:

1,2,71,142

Now, list down the factors of 278

:

1,2,139,278

Greatest Common Factor

We found the factors 142,278 . The biggest common factor number is the GCF number.
So the greatest common factor 142,278 is 2.

Lets's calculate LCM of 224,284

Lowest Common Multiple of 224,284 using Common Division

2 224, 284
2 112, 142
56, 71

∴ So the LCM of the given numbers is 2 x 2 x 56 x 71 = 15904

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15904

Therefore, the GCF of Fractions 142/224,278/284 is 2/15904

Least Common Multiple of 224,284 with GCF Formula

Least Common Multiple of 224,284 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 224,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(224,284) = 4

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

GCF(224,284) x common factors =4 x 1 = 4

LCM(224,284) = ( 224 × 284 ) / 4

LCM(224,284) = 63616 / 4

LCM(224,284) = 15904


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FAQs on GCF of Fractions of 142/224, 278/284

1. What is the HCF of 142,278?

The HCF of 142,278 is 2

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 142/224, 278/284?

Answer: GCF of Numerators as per given numbers 142/224, 278/284 is

GCF of Numerators i.e. for 142,278 is 2

LCM of denominators i.e. for 224,284 is 15904.

Thus, GCF of Fractions is 2/15904.Finally, GCF of Fractions for 142/224, 278/284 is 2/15904.