How to Find GCF of 945/312, 340/284?

GCF of 945/312, 340/284

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 945/312, 340/284 i.e 5/22152 easily. The following is the detailed procedure to determine the greatest common factor of fractions 945/312, 340/284.

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 945/312,340/284?

Given fractions are 945/312,340/284

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 945/312,340/284, numerators are 945,340

Denominators are 312,284

The GCF of 945,340 is 5 .

LCM of 312,284 is 22152.

The greatest common factor of 945/312,340/284 = [GCF of 945,340]/[LCM of 312,284]= 5/22152

Therefore, the GCF of 945/312,340/284 is 5/22152.

Greatest Common Factor of 945,340

To find the highest common factor of 945,340, we have to find the factors of both numbers and list the highest common factor.

The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945

The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340

The HCF of 945,340 is 5.

Lets's calculate GCF of 945,340

Greatest Common Factor (GCF) of 945,340 By Common Division

5	945, 340
	189, 68

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 945,340 By Matching Biggest Common Factor Method

Now, list down the factors of 945

1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945

Now, list down the factors of 340

1,2,4,5,10,17,20,34,68,85,170,340

Greatest Common Factor

We found the factors 945,340 . The biggest common factor number is the GCF number.
So the greatest common factor 945,340 is 5.

Lets's calculate LCM of 312,284

Lowest Common Multiple of 312,284 using Common Division

2	312, 284
2	156, 142
	78, 71

∴ So the LCM of the given numbers is 2 x 2 x 78 x 71 = 22152

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/22152

Therefore, the GCF of Fractions 945/312,340/284 is 5/22152

Least Common Multiple of 312,284 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 312,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(312,284) = 4

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

GCF(312,284) x common factors =4 x 1 = 4

LCM(312,284) = ( 312 × 284 ) / 4

LCM(312,284) = 88608 / 4

LCM(312,284) = 22152

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FAQs on GCF of Fractions of 945/312, 340/284

1. What is the HCF of 945,340?

The HCF of 945,340 is 5

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 945/312, 340/284?

Answer: GCF of Numerators as per given numbers 945/312, 340/284 is

GCF of Numerators i.e. for 945,340 is 5

LCM of denominators i.e. for 312,284 is 22152.

Thus, GCF of Fractions is 5/22152.Finally, GCF of Fractions for 945/312, 340/284 is 5/22152.