How to Find GCF of 714/82, 978/5383?

GCF of 714/82, 978/5383

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 714/82, 978/5383 i.e 6/441406 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/82, 978/5383.

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 714/82,978/5383?

Given fractions are 714/82,978/5383

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 714/82,978/5383, numerators are 714,978

Denominators are 82,5383

The GCF of 714,978 is 6 .

LCM of 82,5383 is 441406.

The greatest common factor of 714/82,978/5383 = [GCF of 714,978]/[LCM of 82,5383]= 6/441406

Therefore, the GCF of 714/82,978/5383 is 6/441406.

Greatest Common Factor of 714,978

To find the highest common factor of 714,978, we have to find the factors of both numbers and list the highest common factor.

The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714

The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978

The HCF of 714,978 is 6.

Lets's calculate GCF of 714,978

Greatest Common Factor (GCF) of 714,978 By Common Division

2	714, 978
3	357, 489
	119, 163

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 714,978 By Matching Biggest Common Factor Method

Now, list down the factors of 714

1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714

Now, list down the factors of 978

1,2,3,6,163,326,489,978

Greatest Common Factor

We found the factors 714,978 . The biggest common factor number is the GCF number.
So the greatest common factor 714,978 is 6.

Lets's calculate LCM of 82,5383

Lowest Common Multiple of 82,5383 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 441406

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/441406

Therefore, the GCF of Fractions 714/82,978/5383 is 6/441406

Least Common Multiple of 82,5383 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 82,5383 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(82,5383) = 1

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

GCF(82,5383) x common factors =1 x 1 = 1

LCM(82,5383) = ( 82 × 5383 ) / 1

LCM(82,5383) = 441406 / 1

LCM(82,5383) = 441406

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FAQs on GCF of Fractions of 714/82, 978/5383

1. What is the HCF of 714,978?

The HCF of 714,978 is 6

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 714/82, 978/5383?

Answer: GCF of Numerators as per given numbers 714/82, 978/5383 is

GCF of Numerators i.e. for 714,978 is 6

LCM of denominators i.e. for 82,5383 is 441406.

Thus, GCF of Fractions is 6/441406.Finally, GCF of Fractions for 714/82, 978/5383 is 6/441406.