How to Find GCF of 756/76, 638/384?

GCF of 756/76, 638/384

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 756/76, 638/384 i.e 2/7296 easily. The following is the detailed procedure to determine the greatest common factor of fractions 756/76, 638/384.

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 756/76,638/384?

Given fractions are 756/76,638/384

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 756/76,638/384, numerators are 756,638

Denominators are 76,384

The GCF of 756,638 is 2 .

LCM of 76,384 is 7296.

The greatest common factor of 756/76,638/384 = [GCF of 756,638]/[LCM of 76,384]= 2/7296

Therefore, the GCF of 756/76,638/384 is 2/7296.

Greatest Common Factor of 756,638

To find the highest common factor of 756,638, we have to find the factors of both numbers and list the highest common factor.

The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756

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

The HCF of 756,638 is 2.

Lets's calculate GCF of 756,638

Greatest Common Factor (GCF) of 756,638 By Common Division

2	756, 638
	378, 319

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

Greatest Common Factor of 756,638 By Matching Biggest Common Factor Method

Now, list down the factors of 756

1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756

Now, list down the factors of 638

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

Greatest Common Factor

We found the factors 756,638 . The biggest common factor number is the GCF number.
So the greatest common factor 756,638 is 2.

Lets's calculate LCM of 76,384

Lowest Common Multiple of 76,384 using Common Division

2	76, 384
2	38, 192
	19, 96

∴ So the LCM of the given numbers is 2 x 2 x 19 x 96 = 7296

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7296

Therefore, the GCF of Fractions 756/76,638/384 is 2/7296

Least Common Multiple of 76,384 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 76,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,384) = 4

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

GCF(76,384) x common factors =4 x 1 = 4

LCM(76,384) = ( 76 × 384 ) / 4

LCM(76,384) = 29184 / 4

LCM(76,384) = 7296

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FAQs on GCF of Fractions of 756/76, 638/384

1. What is the HCF of 756,638?

The HCF of 756,638 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 756/76, 638/384?

Answer: GCF of Numerators as per given numbers 756/76, 638/384 is

GCF of Numerators i.e. for 756,638 is 2

LCM of denominators i.e. for 76,384 is 7296.

Thus, GCF of Fractions is 2/7296.Finally, GCF of Fractions for 756/76, 638/384 is 2/7296.