How to Find GCF of 7/16, 278/19, 316/16?

GCF of 7/16, 278/19, 316/16

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 7/16, 278/19, 316/16 i.e 1/304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7/16, 278/19, 316/16.

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 7/16,278/19,316/16?

Given fractions are 7/16,278/19,316/16

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 7/16,278/19,316/16, numerators are 7,278,316

Denominators are 16,19,16

The GCF of 7,278,316 is 1 .

LCM of 16,19,16 is 304.

The greatest common factor of 7/16,278/19,316/16 = [GCF of 7,278,316]/[LCM of 16,19,16]= 1/304

Therefore, the GCF of 7/16,278/19,316/16 is 1/304.

Greatest Common Factor of 7,278,316

To find the highest common factor of 7,278,316, we have to find the factors of both numbers and list the highest common factor.

The factors of 7 are 1, 7

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

The factors of 316 are 1, 2, 4, 79, 158, 316

The HCF of 7,278,316 is 1.

Lets's calculate GCF of 7,278,316

Greatest Common Factor (GCF) of 7,278,316 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 7,278,316 By Matching Biggest Common Factor Method

Now, list down the factors of 7

1,7

Now, list down the factors of 278

1,2,139,278

Now, list down the factors of 316

1,2,4,79,158,316

Greatest Common Factor

We found the factors 7,278,316 . The biggest common factor number is the GCF number.
So the greatest common factor 7,278,316 is 1.

Lets's calculate LCM of 16,19,16

Lowest Common Multiple of 16,19,16 using Common Division

2	16, 19, 16
2	8, 19, 8
2	4, 19, 4
2	2, 19, 2
	1, 19, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 1 x 19 x 1 = 304

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/304

Therefore, the GCF of Fractions 7/16,278/19,316/16 is 1/304

Least Common Multiple of 16,19,16 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 16,19,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,19,16) = 1

common factors(in case of two or more numbers have common factors) = 16

GCF(16,19,16) x common factors =1 x 16 = 16

LCM(16,19,16) = ( 16 × 19 × 16 ) / 16

LCM(16,19,16) = 4864 / 16

LCM(16,19,16) = 304

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 7/16, 278/19, 316/16

1. What is the HCF of 7,278,316?

The HCF of 7,278,316 is 1

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 7/16, 278/19, 316/16?

Answer: GCF of Numerators as per given numbers 7/16, 278/19, 316/16 is

GCF of Numerators i.e. for 7,278,316 is 1

LCM of denominators i.e. for 16,19,16 is 304.

Thus, GCF of Fractions is 1/304.Finally, GCF of Fractions for 7/16, 278/19, 316/16 is 1/304.