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GCF of 282/77, 638/736

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 282/77, 638/736 i.e 2/56672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 282/77, 638/736.

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 282/77,638/736?

Given fractions are 282/77,638/736

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 282/77,638/736, numerators are 282,638

Denominators are 77,736

The GCF of 282,638 is 2 .

LCM of 77,736 is 56672.

The greatest common factor of 282/77,638/736 = [GCF of 282,638]/[LCM of 77,736]= 2/56672

Therefore, the GCF of 282/77,638/736 is 2/56672.

Greatest Common Factor of 282,638

To find the highest common factor of 282,638, we have to find the factors of both numbers and list the highest common factor.

The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282

The factors of 638 are 1, 2, 11, 22, 29, 58, 319, 638

The HCF of 282,638 is 2.

Lets's calculate GCF of 282,638

Greatest Common Factor (GCF) of 282,638 By Common Division

2 282, 638
141, 319

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

Greatest Common Factor of 282,638 By Matching Biggest Common Factor Method

Greatest Common Factor of 282,638 By Matching Biggest Common Factor Method

Now, list down the factors of 282

:

1,2,3,6,47,94,141,282

Now, list down the factors of 638

:

1,2,11,22,29,58,319,638

Greatest Common Factor

We found the factors 282,638 . The biggest common factor number is the GCF number.
So the greatest common factor 282,638 is 2.

Lets's calculate LCM of 77,736

Lowest Common Multiple of 77,736 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 56672

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/56672

Therefore, the GCF of Fractions 282/77,638/736 is 2/56672

Least Common Multiple of 77,736 with GCF Formula

Least Common Multiple of 77,736 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 77,736 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,736) = 1

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

GCF(77,736) x common factors =1 x 1 = 1

LCM(77,736) = ( 77 × 736 ) / 1

LCM(77,736) = 56672 / 1

LCM(77,736) = 56672


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FAQs on GCF of Fractions of 282/77, 638/736

1. What is the HCF of 282,638?

The HCF of 282,638 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 282/77, 638/736?

Answer: GCF of Numerators as per given numbers 282/77, 638/736 is

GCF of Numerators i.e. for 282,638 is 2

LCM of denominators i.e. for 77,736 is 56672.

Thus, GCF of Fractions is 2/56672.Finally, GCF of Fractions for 282/77, 638/736 is 2/56672.