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GCF of 657/714, 4043/978

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 657/714, 4043/978 i.e 1/116382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 657/714, 4043/978.

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 657/714,4043/978?

Given fractions are 657/714,4043/978

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 657/714,4043/978, numerators are 657,4043

Denominators are 714,978

The GCF of 657,4043 is 1 .

LCM of 714,978 is 116382.

The greatest common factor of 657/714,4043/978 = [GCF of 657,4043]/[LCM of 714,978]= 1/116382

Therefore, the GCF of 657/714,4043/978 is 1/116382.

Greatest Common Factor of 657,4043

To find the highest common factor of 657,4043, we have to find the factors of both numbers and list the highest common factor.

The factors of 657 are 1, 3, 9, 73, 219, 657

The factors of 4043 are 1, 13, 311, 4043

The HCF of 657,4043 is 1.

Lets's calculate GCF of 657,4043

Greatest Common Factor (GCF) of 657,4043 By Common Division

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

Greatest Common Factor of 657,4043 By Matching Biggest Common Factor Method

Greatest Common Factor of 657,4043 By Matching Biggest Common Factor Method

Now, list down the factors of 657

:

1,3,9,73,219,657

Now, list down the factors of 4043

:

1,13,311,4043

Greatest Common Factor

We found the factors 657,4043 . The biggest common factor number is the GCF number.
So the greatest common factor 657,4043 is 1.

Lets's calculate LCM of 714,978

Lowest Common Multiple of 714,978 using Common Division

2 714, 978
3 357, 489
119, 163

∴ So the LCM of the given numbers is 2 x 3 x 119 x 163 = 116382

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/116382

Therefore, the GCF of Fractions 657/714,4043/978 is 1/116382

Least Common Multiple of 714,978 with GCF Formula

Least Common Multiple of 714,978 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 714,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(714,978) = 6

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

GCF(714,978) x common factors =6 x 1 = 6

LCM(714,978) = ( 714 × 978 ) / 6

LCM(714,978) = 698292 / 6

LCM(714,978) = 116382


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FAQs on GCF of Fractions of 657/714, 4043/978

1. What is the HCF of 657,4043?

The HCF of 657,4043 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 657/714, 4043/978?

Answer: GCF of Numerators as per given numbers 657/714, 4043/978 is

GCF of Numerators i.e. for 657,4043 is 1

LCM of denominators i.e. for 714,978 is 116382.

Thus, GCF of Fractions is 1/116382.Finally, GCF of Fractions for 657/714, 4043/978 is 1/116382.