How to Find GCF of 328/13, 312/750?

GCF of 328/13, 312/750

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 328/13, 312/750 i.e 8/9750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 328/13, 312/750.

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 328/13,312/750?

Given fractions are 328/13,312/750

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 328/13,312/750, numerators are 328,312

Denominators are 13,750

The GCF of 328,312 is 8 .

LCM of 13,750 is 9750.

The greatest common factor of 328/13,312/750 = [GCF of 328,312]/[LCM of 13,750]= 8/9750

Therefore, the GCF of 328/13,312/750 is 8/9750.

Greatest Common Factor of 328,312

To find the highest common factor of 328,312, we have to find the factors of both numbers and list the highest common factor.

The factors of 328 are 1, 2, 4, 8, 41, 82, 164, 328

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

The HCF of 328,312 is 8.

Lets's calculate GCF of 328,312

Greatest Common Factor (GCF) of 328,312 By Common Division

2	328, 312
2	164, 156
2	82, 78
	41, 39

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 328,312 By Matching Biggest Common Factor Method

Now, list down the factors of 328

1,2,4,8,41,82,164,328

Now, list down the factors of 312

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

We found the factors 328,312 . The biggest common factor number is the GCF number.
So the greatest common factor 328,312 is 8.

Lets's calculate LCM of 13,750

Lowest Common Multiple of 13,750 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9750

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/9750

Therefore, the GCF of Fractions 328/13,312/750 is 8/9750

Least Common Multiple of 13,750 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 13,750 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,750) = 1

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

GCF(13,750) x common factors =1 x 1 = 1

LCM(13,750) = ( 13 × 750 ) / 1

LCM(13,750) = 9750 / 1

LCM(13,750) = 9750

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FAQs on GCF of Fractions of 328/13, 312/750

1. What is the HCF of 328,312?

The HCF of 328,312 is 8

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 328/13, 312/750?

Answer: GCF of Numerators as per given numbers 328/13, 312/750 is

GCF of Numerators i.e. for 328,312 is 8

LCM of denominators i.e. for 13,750 is 9750.

Thus, GCF of Fractions is 8/9750.Finally, GCF of Fractions for 328/13, 312/750 is 8/9750.