How to Find GCF of 12/31, 28/78, 920/85?

GCF of 12/31, 28/78, 920/85

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 12/31, 28/78, 920/85 i.e 4/205530 easily. The following is the detailed procedure to determine the greatest common factor of fractions 12/31, 28/78, 920/85.

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 12/31,28/78,920/85?

Given fractions are 12/31,28/78,920/85

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 12/31,28/78,920/85, numerators are 12,28,920

Denominators are 31,78,85

The GCF of 12,28,920 is 4 .

LCM of 31,78,85 is 205530.

The greatest common factor of 12/31,28/78,920/85 = [GCF of 12,28,920]/[LCM of 31,78,85]= 4/205530

Therefore, the GCF of 12/31,28/78,920/85 is 4/205530.

Greatest Common Factor of 12,28,920

To find the highest common factor of 12,28,920, we have to find the factors of both numbers and list the highest common factor.

The factors of 12 are 1, 2, 3, 4, 6, 12

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920

The HCF of 12,28,920 is 4.

Lets's calculate GCF of 12,28,920

Greatest Common Factor (GCF) of 12,28,920 By Common Division

2	12, 28, 920
2	6, 14, 460
	3, 7, 230

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 12,28,920 By Matching Biggest Common Factor Method

Now, list down the factors of 12

1,2,3,4,6,12

Now, list down the factors of 28

1,2,4,7,14,28

Now, list down the factors of 920

1,2,4,5,8,10,20,23,40,46,92,115,184,230,460,920

Greatest Common Factor

We found the factors 12,28,920 . The biggest common factor number is the GCF number.
So the greatest common factor 12,28,920 is 4.

Lets's calculate LCM of 31,78,85

Lowest Common Multiple of 31,78,85 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 205530

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/205530

Therefore, the GCF of Fractions 12/31,28/78,920/85 is 4/205530

Least Common Multiple of 31,78,85 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 31,78,85 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,78,85) = 1

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

GCF(31,78,85) x common factors =1 x 1 = 1

LCM(31,78,85) = ( 31 × 78 × 85 ) / 1

LCM(31,78,85) = 205530 / 1

LCM(31,78,85) = 205530

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 12/31, 28/78, 920/85

1. What is the HCF of 12,28,920?

The HCF of 12,28,920 is 4

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 12/31, 28/78, 920/85?

Answer: GCF of Numerators as per given numbers 12/31, 28/78, 920/85 is

GCF of Numerators i.e. for 12,28,920 is 4

LCM of denominators i.e. for 31,78,85 is 205530.

Thus, GCF of Fractions is 4/205530.Finally, GCF of Fractions for 12/31, 28/78, 920/85 is 4/205530.