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GCF of 678/629, 142/364

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 678/629, 142/364 i.e 2/228956 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/629, 142/364.

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 678/629,142/364?

Given fractions are 678/629,142/364

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 678/629,142/364, numerators are 678,142

Denominators are 629,364

The GCF of 678,142 is 2 .

LCM of 629,364 is 228956.

The greatest common factor of 678/629,142/364 = [GCF of 678,142]/[LCM of 629,364]= 2/228956

Therefore, the GCF of 678/629,142/364 is 2/228956.

Greatest Common Factor of 678,142

To find the highest common factor of 678,142, we have to find the factors of both numbers and list the highest common factor.

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

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

The HCF of 678,142 is 2.

Lets's calculate GCF of 678,142

Greatest Common Factor (GCF) of 678,142 By Common Division

2 678, 142
339, 71

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

Greatest Common Factor of 678,142 By Matching Biggest Common Factor Method

Greatest Common Factor of 678,142 By Matching Biggest Common Factor Method

Now, list down the factors of 678

:

1,2,3,6,113,226,339,678

Now, list down the factors of 142

:

1,2,71,142

Greatest Common Factor

We found the factors 678,142 . The biggest common factor number is the GCF number.
So the greatest common factor 678,142 is 2.

Lets's calculate LCM of 629,364

Lowest Common Multiple of 629,364 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 228956

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/228956

Therefore, the GCF of Fractions 678/629,142/364 is 2/228956

Least Common Multiple of 629,364 with GCF Formula

Least Common Multiple of 629,364 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 629,364 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(629,364) = 1

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

GCF(629,364) x common factors =1 x 1 = 1

LCM(629,364) = ( 629 × 364 ) / 1

LCM(629,364) = 228956 / 1

LCM(629,364) = 228956


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FAQs on GCF of Fractions of 678/629, 142/364

1. What is the HCF of 678,142?

The HCF of 678,142 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 678/629, 142/364?

Answer: GCF of Numerators as per given numbers 678/629, 142/364 is

GCF of Numerators i.e. for 678,142 is 2

LCM of denominators i.e. for 629,364 is 228956.

Thus, GCF of Fractions is 2/228956.Finally, GCF of Fractions for 678/629, 142/364 is 2/228956.