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GCF of 566/40, 714/749

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 566/40, 714/749 i.e 2/29960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 566/40, 714/749.

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 566/40,714/749?

Given fractions are 566/40,714/749

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 566/40,714/749, numerators are 566,714

Denominators are 40,749

The GCF of 566,714 is 2 .

LCM of 40,749 is 29960.

The greatest common factor of 566/40,714/749 = [GCF of 566,714]/[LCM of 40,749]= 2/29960

Therefore, the GCF of 566/40,714/749 is 2/29960.

Greatest Common Factor of 566,714

To find the highest common factor of 566,714, we have to find the factors of both numbers and list the highest common factor.

The factors of 566 are 1, 2, 283, 566

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

The HCF of 566,714 is 2.

Lets's calculate GCF of 566,714

Greatest Common Factor (GCF) of 566,714 By Common Division

2 566, 714
283, 357

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

Greatest Common Factor of 566,714 By Matching Biggest Common Factor Method

Greatest Common Factor of 566,714 By Matching Biggest Common Factor Method

Now, list down the factors of 566

:

1,2,283,566

Now, list down the factors of 714

:

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

Greatest Common Factor

We found the factors 566,714 . The biggest common factor number is the GCF number.
So the greatest common factor 566,714 is 2.

Lets's calculate LCM of 40,749

Lowest Common Multiple of 40,749 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 29960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/29960

Therefore, the GCF of Fractions 566/40,714/749 is 2/29960

Least Common Multiple of 40,749 with GCF Formula

Least Common Multiple of 40,749 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 40,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,749) = 1

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

GCF(40,749) x common factors =1 x 1 = 1

LCM(40,749) = ( 40 × 749 ) / 1

LCM(40,749) = 29960 / 1

LCM(40,749) = 29960


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FAQs on GCF of Fractions of 566/40, 714/749

1. What is the HCF of 566,714?

The HCF of 566,714 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 566/40, 714/749?

Answer: GCF of Numerators as per given numbers 566/40, 714/749 is

GCF of Numerators i.e. for 566,714 is 2

LCM of denominators i.e. for 40,749 is 29960.

Thus, GCF of Fractions is 2/29960.Finally, GCF of Fractions for 566/40, 714/749 is 2/29960.