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GCF of 278/400, 418/756

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 278/400, 418/756 i.e 2/75600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/400, 418/756.

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 278/400,418/756?

Given fractions are 278/400,418/756

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 278/400,418/756, numerators are 278,418

Denominators are 400,756

The GCF of 278,418 is 2 .

LCM of 400,756 is 75600.

The greatest common factor of 278/400,418/756 = [GCF of 278,418]/[LCM of 400,756]= 2/75600

Therefore, the GCF of 278/400,418/756 is 2/75600.

Greatest Common Factor of 278,418

To find the highest common factor of 278,418, we have to find the factors of both numbers and list the highest common factor.

The factors of 278 are 1, 2, 139, 278

The factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418

The HCF of 278,418 is 2.

Lets's calculate GCF of 278,418

Greatest Common Factor (GCF) of 278,418 By Common Division

2 278, 418
139, 209

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

Greatest Common Factor of 278,418 By Matching Biggest Common Factor Method

Greatest Common Factor of 278,418 By Matching Biggest Common Factor Method

Now, list down the factors of 278

:

1,2,139,278

Now, list down the factors of 418

:

1,2,11,19,22,38,209,418

Greatest Common Factor

We found the factors 278,418 . The biggest common factor number is the GCF number.
So the greatest common factor 278,418 is 2.

Lets's calculate LCM of 400,756

Lowest Common Multiple of 400,756 using Common Division

2 400, 756
2 200, 378
100, 189

∴ So the LCM of the given numbers is 2 x 2 x 100 x 189 = 75600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/75600

Therefore, the GCF of Fractions 278/400,418/756 is 2/75600

Least Common Multiple of 400,756 with GCF Formula

Least Common Multiple of 400,756 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 400,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(400,756) = 4

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

GCF(400,756) x common factors =4 x 1 = 4

LCM(400,756) = ( 400 × 756 ) / 4

LCM(400,756) = 302400 / 4

LCM(400,756) = 75600


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FAQs on GCF of Fractions of 278/400, 418/756

1. What is the HCF of 278,418?

The HCF of 278,418 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 278/400, 418/756?

Answer: GCF of Numerators as per given numbers 278/400, 418/756 is

GCF of Numerators i.e. for 278,418 is 2

LCM of denominators i.e. for 400,756 is 75600.

Thus, GCF of Fractions is 2/75600.Finally, GCF of Fractions for 278/400, 418/756 is 2/75600.