How to Find GCF of 84/76, 13/79, 319/448?

GCF of 84/76, 13/79, 319/448

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 84/76, 13/79, 319/448 i.e 1/672448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/76, 13/79, 319/448.

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 84/76,13/79,319/448?

Given fractions are 84/76,13/79,319/448

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 84/76,13/79,319/448, numerators are 84,13,319

Denominators are 76,79,448

The GCF of 84,13,319 is 1 .

LCM of 76,79,448 is 672448.

The greatest common factor of 84/76,13/79,319/448 = [GCF of 84,13,319]/[LCM of 76,79,448]= 1/672448

Therefore, the GCF of 84/76,13/79,319/448 is 1/672448.

Greatest Common Factor of 84,13,319

To find the highest common factor of 84,13,319, we have to find the factors of both numbers and list the highest common factor.

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The factors of 13 are 1, 13

The factors of 319 are 1, 11, 29, 319

The HCF of 84,13,319 is 1.

Lets's calculate GCF of 84,13,319

Greatest Common Factor (GCF) of 84,13,319 By Common Division

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

Greatest Common Factor of 84,13,319 By Matching Biggest Common Factor Method

Now, list down the factors of 84

1,2,3,4,6,7,12,14,21,28,42,84

Now, list down the factors of 13

1,13

Now, list down the factors of 319

1,11,29,319

Greatest Common Factor

We found the factors 84,13,319 . The biggest common factor number is the GCF number.
So the greatest common factor 84,13,319 is 1.

Lets's calculate LCM of 76,79,448

Lowest Common Multiple of 76,79,448 using Common Division

2	76, 79, 448
2	38, 79, 224
	19, 79, 112

∴ So the LCM of the given numbers is 2 x 2 x 19 x 79 x 112 = 672448

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/672448

Therefore, the GCF of Fractions 84/76,13/79,319/448 is 1/672448

Least Common Multiple of 76,79,448 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 76,79,448 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,79,448) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(76,79,448) x common factors =1 x 4 = 4

LCM(76,79,448) = ( 76 × 79 × 448 ) / 4

LCM(76,79,448) = 2689792 / 4

LCM(76,79,448) = 672448

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 84/76, 13/79, 319/448

1. What is the HCF of 84,13,319?

The HCF of 84,13,319 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 84/76, 13/79, 319/448?

Answer: GCF of Numerators as per given numbers 84/76, 13/79, 319/448 is

GCF of Numerators i.e. for 84,13,319 is 1

LCM of denominators i.e. for 76,79,448 is 672448.

Thus, GCF of Fractions is 1/672448.Finally, GCF of Fractions for 84/76, 13/79, 319/448 is 1/672448.